Applied / Experimental Physics - Science topic

In the thread rather popular discussion about what "thought” and “real” experiments" are, happens; and it looks as that the position that

- in the discussion is admitted as is correct; this is admitted as is correct in rather numerous other discussions on RG, where non-professional scientists take part, also, though.

The claim really is principally wrong, first of all since there cannot be principally some “purely non-thought experiments”, every real experiment is made aimed at testing of some “purely thought” product – a theory, and so every experimental result isn’t only “some digits on some instruments screens’, the result always is “the digits + interpretation in framework of the theory”

Correspondingly some digits can be interpreted in a number of theories, and the results can be well different, however “confirm”, all theories, etc.

Say, long time experimental “digits” that Sun rotates around Earth well confirmed the theory that Sun rotates around Earth.

Etc. - moreover mainstream physics, first of all the SR?GR are based on postulates that Matter’s spacetime can be impacted by material objects as “space is contracted”, “time is dilated” , “spacetime is curved” [again etc. ] - despite that nobody and never directly observed experimentally any contracted/dilated/ curved spacetime.

At that really, as that rigorously scientifically proven in the Shevchenko-Tokarevsky’s really philosophical 2007 “The Information as Absolute” conception [more see, say, the compact but rather complete consideration of this point in https://www.researchgate.net/publication/387933457_A_response_to_question_What_is_the_The_Information_as_Absolute_conception ] all these postulated in the SR/GR the spacetime properties and effects are some illusory interpretations of real experimental “digits”.

Besides: really “thought experiments” are one of the main obligatory approaches at development and experimental testing of any real theory, including all real experiments before their realizations are made, are made as often numerous “thought experiment” versions, utmost reliable ones are realized as real experiments;.

Again etc., and again moreover – one of principal criteria of any theory validity is that from theory postulates [which are based on experimental digits, however are interpretations of the digits] no any senseless consequences must follow, and this criterion is applied mostly as just “thought experiments”.

One of utmost known now is the Dingle’s “thought experiment” that considers relative motion of two inertial reference frames, from which completely rigorously scientifically it follows that the SR postulates that there is no absolute Matter’s spacetime and that all/every IRF are absolutely equivalent and legitimate are wrong, since from the postulates completely rigorously it follows that both observers in the frames age simultaneously faster and slower each other, what is evident nonsense;

- and, moreover, from this thought experiment so completely rigorously by completely rigorous “Proof by contradiction” follows the really fundamental point in physics that Matter’s spacetime is absolute, etc.

The post is rather long already, so now

Cheers

@ Preston Guynn

Thanks for your kind and detailed response. I have some questions/remarks:

... Are there theoretical attempts from other authors and, if so, how do they match with experiments?

... How was the experimental value determined?

... How do we make sure that the coincidence is not accidental?

PG: "it appears that our galaxy rather than the universe is the relevant factor in a modified Machian principle."

... As the number of galaxies increases with the 3rd power of distance, gravitational potential should mainly build up from the most distant galaxies rather than from nearby masses of our Milky Way galaxy.

PG: "Since the rotation is central to particle structure, then over the dimensions of a macroscopic object, that may well have an effect such as described in your experiment."

... The experiment rather tells something about the possible interaction of accelerating (orbiting) atomic nuclei with large external masses.

It's not necessary to discuss infinitesimals at all, when dealing with quantum computing.The reason is that the Heisenberg-Weyl group does have finite dimensional representations.

why don't you check with blockage corrections in automotive wind tunnel? The blockage problem should not be reduced to the jet expansion effect alone. There is a nozzle effect, a collector effect and a static pressure gradient effect of the empty test section as well (see SAE Technical Paper Series).

Dear Johan!

I want to recommend you papers of my husband)) He study aggregation of blood particals by scanning flow cytometry and also produced (I think, new and fruitfull) kinetic model for this processes. It is his profile https://www.researchgate.net/profile/Vyacheslav-Nekrasov

As I understand, key papers is

1 Brownian aggregation rate of colloid particles with several active sites

2 Kinetic turbidimetry of patchy colloids aggregation: latex particles immunoagglutination

3 Mathematical modeling the kinetics of cell distribution in the process of ligand–receptor binding

4 Kinetics of the initial stage of immunoagglutionation studied with the scanning flow cytometer

But you can write him directly))

Best wishes, Anna

I would suggest to verify the temporal synchronization of the two detectors. For a too narrow coincidence window and different latency of the detectors, the true coincidences might be outside of the coincidence window. Only false (random) coincidences are present. The first step would be to increase the coincidence window to dozens of ns to surely cover any difference in latency. Then you can start decreasing the coincidence window and adding a delay to the fastest detector channel, e.g. using time tagger functionality or simply extending the length of a coaxial cable.

Also, it might be useful to add cut-off filters transmitting the red signal and stopping the blue pump in front of the detectors. Using the filters you make sure that your signal comes from the SPDC process and not from the laser. Filters https://www.semrock.com/filterdetails.aspx?id=blp01-633r-25 are very good but you can use any low-cost alternative.

The ideas are ok but you need to do things that show your summs converge to the integral. Referring to a text on harmonic analysis or numerical analysis would probably be beneficial.

Due to the high pressure and low flow requirements, you should theoretically choose a reciprocating or piston compressor.

In Jansohn, Peter. (2013). Modern Gas Turbine Systems: High Efficiency, Low Emission, Fuel Flexible Power Generation. Oxford. Woodhead Publishing Limited, you can find a guide on how to choose a compressor according to pressure and flow parameters.

Frank T. Edelmann yes sure, thanks for your good discussion. we create this journal based on the other multidisciplinary journal, as example Journal of King Saud University - Science (scopus indexed) publishes peer-reviewed research articles in the fields of physics, astronomy, mathematics, statistics, chemistry, biochemistry, earth sciences, life and environmental sciences.

Other example, PERIÓDICO TCHÊ QUÍMICA (scopus indexed) also publishes peer-reviewed research article in same fields with our journal.

thank you so much for your kind information@ Adel Boumerzoug

Ait Mansour El Houssain thanks a lot for useful tips and guidance. After choosing the title of my paper i will share my experience with all of you thanks again

Hi Abbas

I have the same question! I am trying to fabricate SMF-GIMF-SMF structure for sensor application. I tried many times to splice the fibres. I manipulated with different splicer parameters as prefusion time, overlap, arc power and so on, but almost always I got splice with a black vertical line (fig. 1).

Once I got good splice. It happened when I accidentally broke the bad splice and respliced it again. Unfortunately, I could never repeat it.

At fig.2 you can see two spectrums. The blue one corresponds to SMF-GIMF-SMF with both bad splices. The red one corrensponds to SMF-GIMF-SMF that have one good splice. The second spectrum had a much better contrast then the first one. This is due to the fact that the modes in GIMF fibre are more equally coupled to the SMF fiber. Thus, there is a difference between coupling coefficients of modes in GIFM to SMF fibre for the "bad" and "good" splice.

P.S. Abbas, please, let me know if you will find a method, how to splice it without bubbles and black curves!:)

Dear Sreeprasad

If you are not worried about relative phases and can tolerate a number of very weak secondary beams, perhaps the simplest way is to insert a tilted parallel glass plate into the beam you want to translate. The translation of the main transmitted beam will be Theta*T*(n-1)/n, where n is the refractive index of the glass plate, T is its thickness and Theta is the tilt of the plate's normal relative to the beam propagation direction (in radians). A 1 mm thick glass slide at 5 degrees will result in a shift on order of 50 microns. The main drawback from this method is that more than one beam is transmitted due to the multiple reflections at the glass surface, however the main transmitted beam will be several hundred times more intense than the strongest secondary beam.

Good luck

Yes, we do have to know about the spaces, at least during our university studies, to enables us to expand our mind into abstact level, that will be very usefull for design activities

Thank you very much Dr. Thomas Breuer and Dr. Alaa Faid .

absolutely yes

If you confirmed the formation of ZnO by different experimental tools and you found a decrease in the band gap relative to bulk Zno structure, then, the decrease in the band gap may arise from the formation of crystal defects like oxygen vacancies. You could confirm this interpretation by measuring the fluorescence spectroscopy.

Not of direct help to the question asked, but I offer:

Langford, S. A., and J. K. Nakagawa, 1978. A general equation for estimating refractive indices of Cargille liquids at various temperatures and wavelengths. The Microscope, v. 26, no. 4, pp. 167 - 170.

&

Langford, S. A., 1991. A modified Jelley refractometer. The Royal Microscopical Society J. Microscopy, v. 163, pt. 3, September, pp. 333 - 345. [Please note that the equation on p. 339 requires addition of constant 1.517207, which was inadvertently lost due to an interruption during my final editing work. The correction was published in a later issue, which I can not locate on the Web. --SL, 20 Oct 2016] https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1365-2818.1991.tb03184.x, tinyurl.com/ya9ahlc8.

For purposes of liquid-immersion refractometry [see, for instance, < https://tinyurl.com/yabku63f >] I think that there is no substitute for calibration of liquids soon before they are to be used. Better yet would be the development of an instrument that would continuously log Liquid RIs during liquid-immersion work.

I hope that these thoughts help at least some readers. :-)

-Steve-

@ Xxx Sedao : No, gas shielding alone won't do you any good with this problem as I explained earlier. The oxygen comes form the dissociation of SnO₂ at high temperatures, so you create the oxygen by yourself. Hence, there will be oxygen around even if you work in an inert atmosphere.

To the original question: the two-way speed of light can clearly be measured with no issues: a light beam goes from source A to mirror B at distance L and then back to source A. A clock at A measures the time elapsed and always finds 2L/c, with c independent of reference frame.

So far, this is experiment, well confirmed in many different ways.

One-way speed of light always has some kind of problem, since we need to say when two distant clocks mark the same time. It turns out that it is a consistent convention to assume that clocks can be synchronised in such a way as to make the one-way speed of light constant.

However, to make contact with those who mentioned the Sagnac effect, this consistency only holds in *inertial* reference frames, not in rotating ones. In rotating reference frames, or other non-inertial frames, you generally cannot consistently synchronise clocks in such a way as to have a constant one-way speed of light.

Dear Mr.James Garry

It is just a personal interest,my major study is in a different field.

There are two types of dielectrics, polar and non-polar. Non-polar dielectrics do not have a permanent electric dipole moment, when you apply a field, you generate dipolar moments in the direction of the applied field. You can see the microscopic polarization (the response to the field), as the sum of all the dipolar moments induced. For polar dielectrics, when you applied a field, the pre-existent dipolar moments suffer a torque and tend to align with the applied field, in this case the polarization can now be seen as an average of all the dipoles orientations.

I think when nonlinear refraction is dominant, you can extract the nonlinear parameters from the closed z-scan with some confidence. However, there are cases , for example when either NL refraction or absorption are dominant, that you cannot do that without ambiguity, so that is why it is customary to run the open z-scan to get the NL absorption parameters first, and then used them in the closed-aperture results. Experimentally all you need is a beam splitter in the far field, and an extra detector yo obtain both the open and closed-zscan traces at the same time

Dear Lam Thanh Nguyen:

Thank you for your question, which has introduced me to the Z-Scan technology of which I have previously been completely ignorant. I don't have time to become an expert in your field, but I have just glanced at

My own impression is that as a scientist it is your job to pursue the answers to such questions you have asked by designing your own investigations to achieve the results you seek and to answer for yourself, to your own satisfaction, the questions related to which approaches give you the best information related to the knowledge you seek to gain about nature. Then, to tell others what you've learned and why you believe your work to be useful to others, whether or not your results have confirmed your initial suspicions or taught you some surprising things along the way. 

I have never worried too much about doing things just as others do them routinely. Doing so would make a technologist out of this scientist. Try things out, modify your approaches to fit the need to satisfy your own curiosity, and celebrate the times when you learn something new and think that nobody has done that before.

Your "Why not ...?" makes me think that you may already know the answer to your own question! ;-)

I hope you often enjoy the feeling of success.

Sincerely, -Steve-

Hi Lam,

I had some experience with optical limiting (OL), and my comments about your question are: (i) nonlinear index (NI) could have important effect for OL if the material/structures have resonant features (micro-cavities, photonics crystal etc.) so that intensity at resonant mode(s) or wavelengths is changed with RI. Good design could make OL based on that. (ii) in general cases, OL effects are mostly from nonlinear absorption (NA) (saturable absorption, two photon absorption etc.). Note that, many optical nonlinear materials have both NA and NI. 

Hope that would help. By the way, I will visit HCM city on December, if you have time we can meet there. 

Best,

Dan

On the response function of solid state detectors, based on energetic electron transport processes, X-ray Spectrometry 32 (2003) 458-469

Is SQRT(N) a sufficient measure of the standard uncertainty in x-ray spectroscopy?,X-Ray Spectrom. 2017, 46, 367–373

Quality assurance challenges in x-ray emission based analyses, the advantage of digital signal processing; Invited review paper in Analytical Sciences 21 (2005) 737-745

An alternative approach to the response function of Si(Li) x-ray detectors based on XPS study of silicon and front contact materials, Nucl. Instr. and Meth. A 412 (1998) 109

The Effect of the Signal Processor on the Line Shape Advances in X-Ray Analysis, 53 (2011) 302

This is a long a deep subject.  The short answer is that it requires the material to have both a negative permittivity and negative permeability.  This is called a double-negative material.  There are ways to get a negative refractive in single-negative materials, but those are less studied.  Lots of physics is reversed in negative index materials.  First, it is left-handed instead of right-handed when looking at E, H, and the Poynting vector.  Doppler shift is reversed, Cerenkov radiation is reversed, and more.  

Watch the videos for Lectures 12 and 13 here:

Lots more could be said, but this is a start.

Thank you for your positive comments, Prof.Raul Rangel-Rojo.

dear Lam

in my experience the main source of error in z-scan measurement is the uncertainty in the laser beam fluence measurements, or in other words in the beam shape. As a matter of fact the laser beam is often assumed to be a TEM 00 which is not always realistic. I think this fact can explain the reported differences in the published values and add large uncertainty in the results.

Following Rajeev Gandhi reply, I think it is worth to stress here that measurements using cw sources cannot be compared to pulsed ones since in the first case only the thermo-optical properties are probed. In  fact in this case the signal is originated by the thermo-optical coefficient dn/dT which is not a true third order nonlinear coefficient.

Finally, other techniques for third-order nonlinear characterization may probe other components of the chi^3 tensor, so that the measurements results may be not directly comparable to z-scan results.

Solved!

The link given by Nicolas Guarin-Zapata is not working anymore.

But now there is the Journal of Open Hardware ;-)

"The international peer-reviewed Journal of Open Hardware publishes papers and reviews on technical, legal, economic, and sociocultural aspects of open hardware design, fabrication, and distribution. Its primary goal is to promote research and development of professional, academic, and community-based open hardware projects"

A very simple method would be to put your samples in water, and watch the results:

For density: Archimedes principle (how much water does your sample displace/per weight)

For velocity: Pour your sample in a glass of water of a certain height and record the time it takes the grains to reach the bottom.(maybe use video for this)

From wikipedia: "The cross section is an effective area that quantifies the essential likelihood of a scattering event when an incident beam strikes a target object, made of separate particles."

In other words,be careful when you define transmission as forward scattered light. I would rather say that light is either scattered, absorbed or transmitted. Extinction is defined as the sum of scattering and absorption,

C_ext = C_abs + C_sca,

in scattering cross sections. 

Also, the Stokes parameters describe the light, not scattering by the particle. You will have a set of Stokes parameters for your incident light, and a set of Stokes parameters for the scattered light. Note that the S₀ is really the light intensity! I assume your modulation system describes the relation between the two sets of Stokes parameters i.e. the scattering by your particle (see Mueller Calculus).

Now, an easy way to find the scattering cross section would be to look at the intensities of the incident light and the scattered light:

C_sca = I_sca/I_inc

Just be sure to integrate the scattered intensity over all angles.

This type of behaviour is very common and observed in various properties but its explanation is not too unanimous....

It depends on the density of electrons. If it is more than a value that you can search it, you have to use Fermi Dirac distribution instead of Maxwell boltzmsn distribution function. 

Dear Mohammad,

Thanks for your reply.I already found the solution.I had to rename the file for new project!

1. Judd-Ofelt Theory: Principles and Practices Brian M. Walsh NASA Langley Research Center National Aeronautics and Erice, Italy (June 2005) Space Administration

2. Part I: Principles What is the Judd-Ofelt Theory? Based on static, free-ion and single configuration approximations: • static model - Central ion is affected by the surrounding host ions via a ‘static’ electric field. • free ion model - Host environment treated as a perturbation on the free ion Hamiltonian. • single configuration model - Interaction of electrons between configurations are neglected. The Judd-Ofelt theory describes the intensities of 4f electrons in solids and solutions. The remarkable success of this theory provides a sobering testament to simple approximations. National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

3. Distribution of Citations by Year 200 B.R. Judd, Phys. Rev. 127, 750 (1962). G.S. Ofelt, J. Chem. Phys. 37, 511 (1962). 150 ~ 2000 citations (1962-2004) Number of citations 100 50 0 62 72 82 92 02 Year National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

4. Referenced in 169 Journal Titles Top 20 Titles # of citations PHYSICAL REVIEW B 127 JOURNAL OF NON-CRYSTALLINE SOLIDS 108 JOURNAL OF APPLIED PHYSICS 90 JOURNAL OF CHEMICAL PHYSICS 83 JOURNAL OF ALLOYS AND COMPOUNDS 81 JOURNAL OF LUMINESCENCE 77 JOURNAL OF PHYSICS-CONDENSED MATTER 58 MOLECULAR PHYSICS 57 CHEMICAL PHYSICS LETTERS 48 OPTICAL MATERIALS 43 JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B 38 JOURNAL OF PHYSICS AND CHEMISTRY OF SOLIDS 35 PHYSICA STATUS SOLIDI A-APPLIED RESEARCH 33 OPTIKA I SPEKTROSKOPIYA 30 IEEE JOURNAL OF QUANTUM ELECTRONICS 27 PHYSICS AND CHEMISTRY OF GLASSES 27 OPTICS COMMUNICATIONS 26 SPECTROCHIMICA ACTA PART A 26 INORGANIC CHEMISTRY 24 JOURNAL OF THE AMERICAN CERAMIC SOCIETY 19 National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

5. Prelude “Lanthanum has only one oxidation state, the +3 state. With few exceptions, this tells the whole boring story about the other 14 lanthanides.” G.C. Pimentel & R.D. Sprately, quot;Understanding Chemistryquot;, Holden-Day, 1971, p. 862 http://www.chem.ox.ac.uk/icl/heyes/LanthAct/I1.html ( some amusing mnemonics for the Lanthanides and Actinides) So much for ‘Understanding Chemistry’… Let’s do some physics! National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

6. Ions in Solids Solids • insulators (not semiconductors) • bandgaps are > 5ev (VUV photon) • produce a crystal field Ions • replace host ions substitutionally • transition metal and lanthanide series • unfilled electronic shells • Stark splitting from crystal field • optical transitions occur within bandgap Examples • Nd:Y3Al5O12 - Er:fiber - Cr:Al2O3 (Ruby) National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

7. Atomic Structure of Laser Ions National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

8. Atomic Interactions 4f 95d Hc >> Hso (LS-coupling) Hc << Hso (jj-coupling) Hc ≈ Hso (Intermediate coupling) !1 !2 !3 !4 5S 5I 4f10 5F 4 5I 5 5I 5I Configurations 6 Ho = central field 5I Terms 2S+1 L 7 (Electrons in field 5I Hc = Coulomb field 8 of the nucleus) (Mutual repulsion Levels 2S+1L J of electrons) Hso = spin orbit (Coupling between spin and orbital Stark Levels angular momentum) Vo = crystal field Ho >Hc , Hso >Vo (Electric field of host) Hund’s Rules*: F. Hund, Z. Phys. 33, 345 (1925) 1.) Lowest state has maximum 2S+1 2.) Of these, that with largest L will be lowest 3.) Shells < 1/2 full (smallest J is lowest), Shells > 1/2 full (largest J is lowest) *These rules apply only to the ground state, not to excited states. National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

9. Transitions and Selection Rules • Not all transitions between atomic states that are energetically feasible are quot;allowed”. • Forbidden transitions are “forbidden*” to first order, which means they may occur in practice, but with low probabilities. • Selection rules for transitions depend on type of transition – Electric dipole (E1) – Electric quadrupole (E2) – Magnetic dipole (M1) • Wavefunctions must have correct parity (Laporte’s rule) • Symmetry plays a role in selection rules – Vibronics, crystal field, other perturbing effects. * This nomenclature is historically embedded, although not entirely accurate. National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

10. Multipole Selection Rules ! ! Electric dipole operator (E1) P = quot;e! ri (odd operator) i ! equot; ! ! Magnetic dipole operator (M1) M =quot; ! I i + 2si 2mc i (even operator) ! ! ! ! 1 Q = $ ! k # ri quot;ri 2 i ( ) Quadrupole operator (E2) (even operator) S L J (No 0 ↔ 0) Parity Electric Dipole ΔS = 0 ΔL= 0, ±1 ΔJ = 0, ±1 opposite Magnetic dipole ΔS = 0 ΔL= 0 ΔJ = 0, ±1 same Electric quadrupole ΔS = 0 ΔL = 0, ±1, ±2 ΔJ = 0, ±1, ±2 opposite National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

11. A Brief History of Parity Otto Laporte (1902-1971) empirically discovered the law of parity conservation in physics. He divided states of the iron spectrum into two classes, even and odd, and found that no radiative transitions occurred between like states: O.Laporte, Z. Physik 23 135 (1924). Eugene Paul Wigner (1902-1995) explicitly formulated the law of parity conservation and showed that Laporte’s rule is a consequence of the invariance of systems under spatial reflection. E. P. Wigner, “Gruppentheorie und Ihre Anwendung auf die Quantenmechanik der Atomspektren”. Braunschweig:F. Vieweg und Sohn, 1931. English translation by J. J. Griffin. New York: Academic Press, 1959. Wavefunctions are classified as even (+1 parity) or odd (-1 parity). By convention, the parity of a photon is given by the radiation field involved: ED ( -1), MD (+1). For mathematical reasons, the parity of any system is the product of parities of the individual components. If the initial and final wavefunction have same parity (±1): ED: ±1 = (-1)(±1) Parity is NOT conserved. Transition is forbidden! MD: ±1 = (+1)(±1) Parity IS conserved. Transition is allowed! Laporte Rule: States with even parity can be connected by ED transitions only with states of odd parity, and odd states only with even ones. National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

12. Parity Selection Rules ED allowed ED forbidden MD forbidden MD allowed EQ forbidden EQ allowed s → p s → s p → d d → d d → f p → p f → g f → f s → f g → g p → g Orbital s p d f g Angular momentum ! 0 1 2 3 4 !- odd # electrons ! = ( quot;1)# i ! even odd even odd even !- even # electrons i odd even odd even odd National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

13. Historical Perspective I • J.H. Van Vleck - J. Phys. Chem. 41, 67-80 (1937) (The Puzzle of Rare-Earth Spectra in Solids) – Why are spectral lines in rare earths observable? – Electric dipole(E1), magnetic dipole(M1), quadrupole(E2)? – Concludes a combination is possible. – Suggests that crystal field makes mixed parity states (E1). • L.J.F. Broer, et al., - Physica XI, 231- 250 (1945) (On the Intensities and the multipole character in the spectra of the rare earth ions) – Considers all mechanisms. – Concludes quadrupole radiation is too weak. – Considers magnetic dipole , but as a special case only. – ED transitions dominate as suggested by Van Vleck! National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

14. Historical Perspective II • G. Racah - Phys. Rev. 76, 1352 (1949) (Theory of Complex Spectra IV) – Applies group theory to problems of complex spectra – Creates the tools required to make detailed spectroscopic calculations involving states of the 4f shell. – Revolutionizes the entire subject of rare earth spectroscopy. • Subsequent developments – Racah’s methods applied to crystal field theory. – Ideas of Racah applied to transition metal ions (Griffiths). – Practical calculations assisted by computer generated tables of angular momentum coupling coefficients. • By 1962 the stage was set for the next major development: The Judd-Ofelt theory of the intensities of RE transitions. National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

15. The Stage is Set “I suggest that the coincidence of discovery was indicative that the time was right for the solution of the problem.” Brian G. Wybourne “The fascination of rare earths - then, now and in the future” Journal of Alloys and Compounds 380, 96-100 (2004) National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

16. Judd and Ofelt Publish (1962) National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

17. States of an Ion in the Crystal The Crystal field, V, is considered as a first order perturbation that ‘admixes’ in higher energy opposite parity configurations: } quot;a V quot;# ! a = quot;a + % quot;# # Ea $ E# Mixed Parity quot;# V quot;b States ! b = quot;b + % quot;# # Eb $ E# ! ! ! ( +a V +* quot; + * P +b + a P + * + * V +b % quot; ,a P,b = !' + $ * quot; & Ea ) E * Eb ) E* quot; # φa and φb have the same parity (4f N states) φβ has opposite parity (4f N-15d states) V is the crystal field (treated as a perturbation) ! P is the electric dipole operator National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

18. Tensor Forms of Operators Racah defined irreducible tensors, C(k), which transform as spherical harmonics, having the components: quot; 4! % 1/2 Cq ) (k =$ # 2k + 1 ' Ykq & The position vector r is a tensor of rank 1, defined as r = rC (1) Dipole Operator Crystal Field ! ! Standard Form P = quot;e! ri V = ! ! Akq ri kYkq (quot; i , # i ) i i kq Dq = !equot; ri #Cq % D p ) = ! Atp ! rit quot;C p ) $ (1) (1) (t (t Tensor Form $ & i # % i i tp i Note: t is odd since only odd order terms contribute to parity mixing. Even order terms are responsible for energy level splitting. National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

19. J-O Theory Assumptions 1&2 1.) The states of φβ are completely degenerate in J. Assume an average energy for the excited configuration above the 4fN, that is, the 4f N-15d. 2.) The energy denominators are equal ( Ea-Eβ = Eb-Eβ ) Assume that the difference of average energies, ΔE(4f-5d), is the same as the difference between the average energy of the 4f N-15d and the energy of the initial and final states of the 4fN These assumptions are only moderately met, but offer a great simplification. Otherwise, the many fold sum of perturbation expansions is not suitable for numerical applications. National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

20. 4f and 4f N N-15d configurations 35 4fn configuration 30 4fn-15d1 configuration 25 Energy(×104cm-1) 20 Lanthanides in YLF: K. Ogasawara et al., 15 J. Solid State Chem. vol. 178, 412 (2005 10 5 0 Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb 58 59 60 61 62 63 64 65 66 67 68 69 70 Atomic Number & Symbol National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

21. Advantages of the Assumptions I.) Energy denominators can be removed from the summations II.) Closure can be used ( the excited configuration forms a complete orthonormal set of basis functions) #! quot; !quot; = 1 quot; III.) Angular parts of the electric dipole operator and crystal field Cq = ! C (1) !! U q (1) (1) and C p ) = ! C (t ) !! U p ) (t (t can be combined into an effective tensor operator %t 1 quot; ( + t 1 quot; . (quot; ) U U (1) (t ) = # (!1) 1+t + quot; +Q (2 quot; + 1) & )- 0 UQ ' ! ! !$ * , p q Q / q p quot;Q The 3j symbol ( ) is related to the coupling probability for two angular momenta. The 6j symbol { } is related to the coupling probability for three angular momenta. The Wigner 3-j and 6-j symbols are related to Clebsch-Gordon coupling coefficients. National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

22. Reduced Matrix Elements Nevertheless, combining the tensors for the electric dipole and crystal field terms in a combined tensor operator, UQ! ) , ( can be simplified further by the Wigner-Eckart Theorem: Geometry Physics (transformations) (Dynamics) % J quot; J# ( N f N! JM UQquot; ) f N! # J #M # = ($1)J $ M ' ( f ! J U ( quot; ) f N! # J # & $M Q M #* ) The matrix elements on the right side have been tabulated: “Spectroscopic Coefficients of the p N, d N, and f N Configurations,” C.W. Nielson and G.F. Koster, M.I.T Press, Cambridge, MA (1963). The 3-j and 6-j symbols have also been tabulated: “The 3-j and 6-j symbols,” M. Rotenberg, R, Bivens, N. Metropolis, J.K. Wooten Jr., Technology Press, M.I.T, Cambridge, MA (1959). National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

23. “Full Judd-Ofelt Theory” ! 1 * * J( $ () 1)J )M )Q (2* + 1)AtpY (t , * )' t $' J , a P , b = )e!! % %q Q quot;% quot; + a U ( * ) +b tp *Q & p quot;% ) M #& Q M (quot; # n! r nquot;!quot; nquot;!quot; r t n! &1 t ! ) Where, Y (t, ! ) = 2% ! C (1) !quot; !quot; C (t ) ! ' * n! Ea # E$ ( ! !quot; ! + This is the “Full Solution” of the Judd-Ofelt Theory. This form can be used to find electric dipole matrix elements between mixed parity states for individual Stark level to Stark level transitions. Application of “Full Judd-Ofelt Theory”: R.P. Leavitt and C.A. Morrison, “Crystal-field Analysis of triply Ionized lanthanum trifluoride. II. Intensity Calculations.” Journal Of Chemical Physics, 73, 749-757 (1980). National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

24. J-O Theory Assumptions 3&4 Oscillator strength (f-number) for electric dipole transition: 2 8+ mc 2 (n + 2% 2 ! ! 2 f = n& & 3n ## )JM P ) quot;J quot;M quot; 3quot;* (2 J + 1)e 2 ' $ L.J.F. Broer, et al., - Physica XI, 231- 250 (1945) 3.) Sum over Stark split J-levels (Assumes all Stark levels equally populated) $ J ! Jquot; ' $ J !quot; J quot; ' 1 *& Q M quot; ) & #M = + + Qquot; M quot; ) 2 ! + 1 !! quot; QQ quot; M = -J, -(J-1), …, 0, …, (J-1), J MM quot; % #M (% ( 4.) Sum over dipole orientations (Assumes optically isotropic situation) quot;1 ! t % quot;1 ! t) % 1 ($ q Q p' $ q Q = * * p) ' 2t + 1 tt ) pp ) Q = 0 (π-polarized, E ⊥ c) Q # &# & Q = ±1 (σ-polarized, E || c) National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

25. “Approximate Judd-Ofelt Theory” 2 2 8! mc 2 # n + 2& 2 Atp ) )) 2 (quot; ) f = n% (2 quot; + 1) Y (t, quot; ) * a U 2 *b 3hquot; (2J + 1) $ 3n ( ' quot; = 2, 4,6 p t =1, 3,5 (2t + 1) 2 Atp Defining Ωλ as: !quot; = (2 quot; + 1)# # (2t + 1)Y 2 (t, quot; ) Judd-Ofelt p t =1, 3,5 parameters 2 8! 2 mc # n2 + 2 & + 2 (quot; ) f = n% )quot; * a U *b Oscillator 3hquot; (2J + 1) $ 3n ( ' quot; = 2, 4,6 strength $ 2 (quot; ) SED = !quot; # a U #b is called the Linestrength. quot; = 2, 4,6 This is the “Approximate Solution” of the Judd-Ofelt theory. It can be used to find electric dipole matrix elements between mixed parity states for manifold to manifold transitions. National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

26. Judd-Ofelt Parameters In principle, the Judd-Ofelt parameters can be calculated “ab-initio” if the crystal structure is known, and hence, Atp: 2 Atp !quot; = (2 quot; + 1)# # Y 2 (t, quot; ) p t =1, 3,5 (2t + 1) n! r nquot;!quot; nquot;!quot; r t n! &1 t ! ) Y (t, ! ) = 2% ! C !quot; !quot; C ! ' (1) (t ) * n! Ea # E$ ( ! !quot; ! + # ! 1 !! & ! C (1) !! = (quot;1)! % ( 2! + 1)1/2 ( 2!! + 1)1/2 $0 0 0( ' # !! t ! & ! C (t ) !! = (quot;1)!! % ( 2!! + 1)1/2 ( 2! + 1)1/2 $ 0 0 0( ' 3-j and 6-j symbols can be calculated for ! = 3 (4f ) and !! = 2 (5d) Radial integrals between configurations and crystal field components, Atp, are difficult to calculate. Instead, Judd-Ofelt parameters are usually treated as phenomenological parameters, determined by fitting experimental linestrength data. National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

27. Intermission “The two papers of 1962 represent a paradigm that has dominated all further work on the intensities of rare earth transitions in solutions and solids up to the present time.” Brian G. Wybourne “The fascination of rare earths - then, now and in the future” Journal of Alloys and Compounds 380, 96-100 (2004). National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

28. Part II: Practices The Judd-Ofelt theory, in practice, is used to determine a set of phenomenological parameters, Ωλ (λ=2,4,6), by fitting the experimental absorption or emission measurements, in a least squares difference sum, with the Judd-Ofelt expression. Absorption Least Squares Judd-Ofelt Collect Matrix Measurements Fitting Parameters Elements # ( )=0 ! quot;2 Ωλ manifold ! (quot; )d quot; |<U(λ)>|2 !# k Transition τr and β Probabilities AJ′J The Judd-Ofelt parameters can then be used to calculate the transition probabilities, AJ′J, of all excited states. From these, the radiative lifetimes, τr, and branching ratios, β, are found. National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

29. Selection Rules Revisited ! j1 j2 j3 $ #1 t ! & ! j1 j2 j3 $ $ J ! Jquot; ' quot; %=0 $ ' #m =0 #! 1 !2 !3 & ! !quot; ! ( quot; 1 m2 m3 & % & #M % Q M quot;) ( % Unless: Unless: J! quot; J # $ ! = 2, 4, 6 ji ! 0 ji ! 0 t = 1, 3, 5, 7 !J quot; 6 !i ! 0 mi quot; ji ! quot;1+ t !L quot; 6 j1 quot; j2 # j3 # j1 + j2 m1 + m2 + m3 = 0 !S = 0 !! quot; ! # 1 ji , mi (1, 1/2 integer) ! 2 quot; ! 3 # j1 # ! 2 + ! 3 J = 0 : J # $ even Only d or g j1 # j2 quot; j3 quot; j1 + j2 ! 1 quot; ! 3 # j2 # ! 1 + ! 3 orbitals can J # = 0 : J $ even mix parity ! 1 quot; ! 2 # j3 New Selection Rules From Judd-Ofelt Theory S L J (No 0 ↔ 0) Parity Electric Dipole ΔS = 0 ΔL ≤ 6 ΔJ ≤ 6 opposite ΔJ = 2,4,6 (J or J′ = 0) Magnetic dipole ΔS = 0 ΔL = 0 ΔJ = 0, ±1 same Electric quadrupole ΔS = 0 ΔL = 0, ±1, ±2 ΔJ = 0, ±1, ±2 opposite National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

30. Judd-Ofelt Analysis I Matrix Forms 3ch(2J + 1) # 3 & 2 Sm = 8! e quot; 3 2 n% 2 $ n + 2( ' * manifold ) (quot; )d quot; S jm Components of 1 x N matrix 3 $ S = quot; M ij !i 2 (quot; ) SED = !quot; # a U #b t j quot; = 2, 4,6 i =1 N = number of tramsitions Mij - components of N x 3 matrix for square matrix elements of U ( 2 ), U ( 4 ), U (6 ) Ωi - components of 1 x 3 matrix for Judd-Ofelt parameters Ω 2, Ω 4, Ω 6 2 N % m 3 ( ! = $ ' S j quot; $ M ij #i * 2 LEAST SQUARES DIFFERENCE j =1 & i =1 ) ( ) = $2 ! quot;2 N & m 3 ) ( !(0) = M †M ) quot;1 !# k % ' M jk ( S j $ % M ij #i + = 0 MINIMIZED * M †Sm j =1 i =1 Judd-Ofelt Parameters 1 x 3 Matrix National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

31. Judd-Ofelt Fit (Ho:YLF) 6.0 Visible absorption spectrum of Ho:YLF 5.0 !ab (10-20 cm2) (! and quot; polarization) 4.0 3.0 2.0 1.0 0.0 280 330 380 430 480 530 580 630 680 Wavelength (nm) National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

32. Judd-Ofelt Analysis II With the Judd-Ofelt parameters, the ED transition probability for any excited state transition (J´→ J) can be calculated 64quot; 4 e2 * $ n2 + 2 ' 2 - Transition probability A J !J = 3 ,n & SED + n SMD / 2 3h(2 J ! + 1)# , % + 3 ) ( / . (Einstein A coefficient) 1 = # AJ quot;J Radiative lifetime !r J (natural decay time) AJ quot;J Branching ratio ! J quot;J = # AJ quot;J (fraction of total photon flux) J MD transitions are normally orders of magnitude smaller than ED transitions. Since ED transitions for ions in solids occur as a result of a perturbation, some MD transitions will make significant contributions. National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

33. Magnetic Dipole Contributions Magnetic dipole contributions can be easily calculated using an appropriate set of intermediate coupled wavefunctions for transitions obeying the selection rules ( ΔS = 0, ΔL= 0, ΔJ = 0, ±1). 2 ' quot; $ ! ! f n [SL]J L + 2S f n [S !L!]J ! 2 S MD =% quot; MD Linestrength & 2mc # 1/ 2 LS-coupled 2 - (J + 1) . (L . S ) * ! ! ! n '- ! 2 2 *$ f [SL]J L + 2 S f [S /L/]J / = &+(S + L + 1) . (J + 1) + matrix elements n 2 ((# !+ %, , 4(J + 1) )(! )quot; G.H. Shortley Phys. Rev. 57, 225 (1940) Intermediate coupled wavefunctions f n [SL]J = ! C ( S, L ) f n SLJ SL (linear combination of LS states) ! ! n quot; ! n f [SL]J L + 2S f [S quot;Lquot;]J quot; = n ! C (S , L )C (S , L ) f SLJ L + 2S f S quot;Lquot;J quot; n SL ,S quot;Lquot; Intermediate coupled matrix elements National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

34. Judd-Ofelt Results (Ho:YLF) National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

35. Testing the J-O theory Branching ratios can be measured directly from emission spectra. Use reciprocity of emission and absorption to indirectly “measure” the radiative lifetimes. Z! *$ hc ' - ! em ( quot; ) = ! ab ( quot; ) exp ,& EZL # ) kT / D.E. McCumber Zu +% quot;( . Phys. Rev. 136, A954 (1964). By comparing the measured emission cross section quot;5 3I& ( quot; ) ! (quot; ) = P. Moulton 8# cn 2 ($ r / % ) + ' 2I ! ( quot; ) + I # ( quot; ) ) quot; d quot; ( * J. Opt. Soc Am. B 3, 131 (1986). with the emission cross section derived from absorption, the quantity (τr/β) can be determined and the radiative lifetime extracted for comparison with the Judd-Ofelt theory National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

36. Reciprocity of Ho:YLF (5I7 ↔ 5I8) National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

37. Accuracy of J-O theory (Ho&Tm) Results are somewhat better in Ho3+ than Tm3+. Overall, the accuracy of the Judd-Ofelt theory is quite good, despite the approximations used. National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

38. Special Case I: Pr3+ ion (A failure of the standard Judd-Ofelt theory?) Pr3+ ions suffer from several problems in applying Judd-Ofelt theory 1.) Large deviations between calculations and experiment observations. 2.) Negative Ω2 sometimes obtained, in opposition with definition. 3.) Ω2, Ω4, Ω6 highly dependent on transitions used in fit. These inconsistencies are usually explained by the small energy gap (~ 50,000 cm -1) between the 4f N and 4f N-15d configurations in Pr3+ Solutions: 1.) Modify the standard theory: quot;!# = quot;# &1 + ( $Eij % 2E4 f ) ( E5d % E4 f ) ( ' 0 ) E.E. Dunina, et al., Sov. Phys. Solid State 32, 920 (1990). 2.) Remove 3H4 → 3P2 from the fit, or augment fit with fluorescence β’s R.S.Quimby, et al., J. Appl. Phys. 75, 613 (1994). 2 N +% ( . 3.) Use normalized least squares fitting procedure: ! = $ -' S jm quot; $ M ij #i * ! i 0 2 j =1 , & i ) / P. Goldner, et al., J. Appl. Phys. 79, 7972 (1996). National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

39. Special Case II: Eu3+ ions (Beyond the standard Judd-Ofelt theory)  The ED transitions 7F0 ↔ 5DJodd, 7FJodd ↔ 5D0 and 7F0 ↔ 5D0 in Eu3+ are “forbidden” in standard JO-theory. They violate the selection rules: • ΔS = 0 G.W. Burdick, J. Chem Phys. 91 (1989). • If J = 0 then J′ is even • If J′ = 0 then J is even M. Tanaka, Phys. Rev. B, 49, 16917 (1994). •0↔0 T. Kushida, Phys. Rev B, 65, 195118 (2002).  These transitions are primarily MD, but all three do occur as ED with low intensity in the spectra of some materials.  This implies that the standard Judd-Ofelt theory is incomplete. These ‘forbidden’ transitions provide an ideal testing ground for extensions to the standard theory.  What mechanism or mechanisms could be responsible? Are they meaningful! National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

40. Europium’s Peculiar Properties (Adventures of The Atom) The Atom, Issue 2 August 1962 (DC Comics) Coincident with the publications of Judd and Ofelt, who were both also interested in Europium’s peculiar properties. National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

41. Extensions I 1) J-mixing: The wavefunctions of the J ≠ 0 state are mixed into the J = 0 state by even parity terms of the crystal field. Explains the radiative transition 7F3 ↔ 5D0 in Eu3+. J.E. Lowther, J. Phys. C: Solid State Phys. 7, 4393 (1974). 2) Electron correlation: Electrostatic interaction between electrons is taken into account. Goes beyond the single configuration approximation and electron correlation within the 4f shell is incorporated by configuration interactions. Contributes to “allowing” the “forbidden” 0 ↔ 0 transitions such as 7F0 ↔ 5D0 in Eu3+. K. Jankowski, J. Phys B: At. Mol. Phys. 14, 3345 (1981). 3) Dynamic coupling: The mutual interaction of the lanthanide ion and the crystal environment are taken into account. Goes beyond the static coupling model. Explains hypersensitive transitions (transitions highly sensitive to changes in environment). M.F. Reid et al., J. Chem Phys. 79, 5735 (1983). National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

42. Extensions II 4) Wybourne-Downer mechanism: Involves spin-orbit interaction among states of the excited configurations, leading to an admixing of spin states into the 4f N configuration. This accounts for the observed spin “forbidden” transitions ΔS = 1 B.G. Wybourne, J. Chem. Phys. 48, 2596 (1968). M.C. Downer et al., J. Chem. Phys 89, 1787 (1988). 5) Relativistic contributions: Relativistic treatment of f → f transitions in crystal fields. Reformulation of crystal field and operators in relativistic terms. Importance unknown. L. Smentek, B.G. Wybourne, J. Phys. B: At. Mol. Opt, Phys. 33, 3647 (2000). L. Smentek, B.G. Wybourne, J. Phys. B: At. Mol. Opt, Phys. 34, 625 (2001). Review Articles Early development: R.D. Peacock, Structure and Bonding, vol. 22, 83-122 (1975). Later developments L. Smentek, Physics Reports, vol. 297, 155-237 (1998). National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

43. Summary Physical Mechanisms: (Not a complete list)  Crystal field influence based on static model. Second order in the perturbation. (This is the standard Judd-Ofelt theory).  Crystal field influence based on static and dynamic model. Second order.  Electron correlation based on static and dynamic model. Third order.  Spin-orbit interaction. Intermediate coupling and Third order effects.  Relativistic effects. Remaining Problems:  Estimating the relative importance of each mechanism is considerable. (Many competing mechanisms producing various effects. Entangled situation)  Ab-initio calculations still not entirely successful. - Theory of f - f transitions not yet complete. - Calculation of Radial integrals and knowledge of odd crystal field parameters. - Vibronics (Vibrational lattice-ion coupling)  Multitude of mechanisms and new parameters abandons simplicity. - Simple linear parametric fitting to observed spectra is lost. - Physically meaningful descriptions can be obscured. National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

44. What’s next? “It has been in a very real sense the first step in the journey to an understanding of the rare earths and their much heavier cousins, the actinides, but like many journeys into the unknown, the end is not in sight.” Brian G. Wybourne “The fascination of rare earths - then, now and in the future” Journal of Alloys and Compounds 380, 96-100 (2004). National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

45. Judd and Ofelt Finally Meet 40 years after publications B.R. Judd G.S. Ofelt B.G. Wybourne Ladek Zdroj,Poland - June 22, 2003 “4th International Workshop on Spectroscopy. Structure and Synthesis of Rare Earth Systems.” National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

46. 2007 School of Atomic and Molecular Spectroscopy 2007 will be the 45th anniversary of the simultaneous publications of Brian Judd and George Ofelt. A special session is certainly worth considering in the next course. “The fascination of the Rare Earths - 45th Anniversary of Judd-Ofelt theory” Possible invited lecturers: Brian R. Judd - The Johns Hopkins University, Baltimore, MD 21218, USA E-mail: juddbr@eta.pha.edu George S. Ofelt - 824 Saint Clement Road, Virginia Beach, VA 23455, USA E-mail: gsofelt@pilot,infi,net Lydia Smentek - Vanderbilt University, Box 1547, Station B. Nashville, TN 37235, USA E-mail: sementek1@aol.com G.W. Burdick - Andrews University, Berrien Springs, MI 49104, USA E-mail: gburdick@andrews.edu Francois Auzel -UMR7574, CNRS, 92195 Meudon Cedux, France E-mail: francois.auzel@wanaoo.fr Sverker Edvardsson, Mid Sweden University, S-851 70, Sundsvall, Sweden E-mail: Sverker.Edvardsson@mh.se National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

47. Acknowledgements Rino DiBartolo- Thank you for your years of wisdom and my first lecture on Judd-Ofelt theory in your office in ‘old’ Higgins Hall. Also for inviting me to Erice these last 10 years. Norm Barnes- Thank you for helping me see the laser side of life. The discussions we have had over the years remain with me. National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

48. Dedication Brian G. Wybourne (1935-2003) Professor Brian G Wybourne Commemorative Meeting: Symmetry, Spectroscopy and Schur Institute of Physics, Nicolaus Copernicus University, Torun, Poland June 12-14, 2005. A commemorative meeting in honor of Professor Brian G. Wybourne will be held in Torun, Poland from 12-th to 14-th June 2005. The aim is to celebrate Brian's academic life and his contributions to many aspects of physics and mathematics. This meeting will bring together friends, students, collaborators of Brian as well as people interested in the results and consequences of his research. National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

49. National Aeronautics and Erice, Italy (June 2005) Space Administration

50. National Aeronautics and International School of Atomic and Molecular Spectroscopy Space Administration Erice, Italy (June 2005)

What Abdallah has said is absolutely right.

A standard example is the binding energy calculation of He⁴. It is made out of two protons and two neutrons. Masses are measured in atomic mass units where carbon is a reference point. One u is mass of carbon atom/12.

Mass of two protons is 2x1.00728=2.01456 u.

Mass of two neutrons is 2 x 1.00866=2.01732 u.

Mass of two electrons= 2 x 0.000549 = 0.001098 u.

total mass is 4.032978 u.

mass of the alpha particle is, 4.00153 u, that is the difference is 0.031448 u. Therefore the binding energy of alpha particle is 0.031448 x 931.5=29.29 MeV (approx). If you do not like to include masses of the electrons then the defect is 0.03035 u. This corresponds to a binding energy of 28.27 MeV (approx).

Dear dr. Ilian Peruhov,

about your first question, Robert Pohl (https://en.wikipedia.org/wiki/Robert_Pohl) devised a a working mechanical analogy between a sprinkler and spin transitions, which he included in the 1975 German edition of his book “Elektrizitätslehre”. I attach the pages I refer to. Abb. 14.14 shows the device on which the analogy is based. However, this mechanical analogy is not shown in every edition of Pohl's book.

While Larmor precession is a classical explanation of why matter shows a magnetic moment when in a magnetostatic field, NMR is a way of measuring the free induction decay (FID) response of diamagnetic substances (in solution). Whatever explanation is given for diamagnetism, the main problem when trying to visualize Larmor's precession of spin is that the spin itself is not a classically visualizable property. Thus, I would say that the directly observed quantity is the FID, indeed.

As for the directivity of magnetized needles, that remarkable property belongs to a small class of substances. The majority of matter is only slightly affected by magnetic fields, and one needs strong fields to observe tiny effects. Finally, you should keep in mind that, although NMR instruments have a spot where the field is homogeneous, generally strong magnetic fields are a bit non-homogeneous.

Dear  Jafary, nonlinear  grows of temperature with  pulse energy absorbance is main reason of your observation. The  phenomena has  been studied well. I provide You some conclusion from review paper:"Absorptivity as a function of temperature is an important consideration in practice and is usually modelled successfully as a linear function except around the melting point of the metal where there is a significant jump due to the sudden change of conduction electron density".

There's no difficulty in simulating the double slit diffraction pattern, to any precision, whether in the Fraunhofer approximation, the Kirchhoff formulation-in classical electrodynamics-or by solving the problem in quantum mechanics. And it's a standard lab experiment in wave optics.

In another approach, it might be mode softening of the particular mode with pressure. If this is the case how one can explain it. Please comment on this.

Hello, Narasim!

I'm not a physic but I also had a chilling feeling while listening to this news. The first thing I realized that this was the event that A. Einstein predicted about 100 years ago by theoretical background and, lastly, it was proved practically last week. For deep understanding, I dug up to some resources, mostly popular, and found my favorites:

The main prospective from it, in my point of view (that based on my survey), is an appearance of drastically new technique to investigate time and space and something else. Some compare it "to a deaf person suddenly gaining the ability to hear sound. An entirely new realm of information is now available.".

For me. the best striking strings about gravitational waves are the next:

"When asked to comment on LIGO's impact on the world beyond the scientific community, and about how gravitational-wave science might influence people's daily lives, Reitze simply said, "Who knows?"

"When Einstein predicted general relativity, who would have predicted that we'd use it every day when we use our cellphones?" he said. (General relativity provides an understanding how gravity influences the passing of time, and this information is necessary for GPS technology, which uses satellites that orbit further away from the gravitational pull of the Earth than people on the surface)."

Anyway, such a breakthrough gives all scientists much anticipations and hopes for their work (in any field of interests) and also is promoting science as the whole to a wide range of society. 

Best regards.

I agree with Gregory if "electron beam melting" means the technology of part manufacturing by selective electron beam melting of metal powder. In that case high vacuum is strictly recommended to avoid electron beam scattering and related electron beam defocusing effect. So you have to maintain vacuum to produce precise and high quality parts. But in some other technologies based on electron beam melting, zone refining for instance, different volumes are used for electron accelerator and production chamber, separated by the foil. Most commonly used material for the foil to extract electron beams of relatively low energy (200 kV or so) are aluminium and titanium - light metals with relatively long free-path length of electrons.

there is a very simple although less scientific method: Just take a business card and shake it along the beam in a dark room. If the laser is pulsed, you will see a line of dots, just because your pulse "ketches" the card in different locations. That works with rep-rates up to several kHz. For rep-rates faster, you will need a fast detector.

In general every plasma can be inhomogenious and thus have spatial dependent refractive index fields (I was assuming a homogenious plasma, because if the plasma is inhomogenious the trivial answer is that you cannot do anything about focussing or defocussing as the electron density changes from point to point and hence also the refractive index - that can usually be not compensated by any power modulation of your beam).

Secondly not every nonlinearity does automatically lead to a refraction of your beam. Furthermore first you wrote that the beam has to have enough energy that the non linearities of the plasma come into play and then you claim that it is this non linearities, which (de)focus the laser beam - this is not really stringent.

The power and the timescale of the laser beam are also correlating, because due to energy conservation it holds that the shorter the beam temporally (at a given pulse energy) the higher is the power, you can deposit. However, non linearities come into play per definition at high amplitudes of your electromagnetic fields (the type of non linearity is hereby secondary).

So, you cannot say that you have just to go to higher laser powers in order to avoid self (de)focusing of your beam. Also the power density per unit area of the beam is proportional to the |E|² of your laser, which I also covered in my first post here.

So, in conclusion I want to emphasise again, the straight forward way to avoid optical effects in a plasma is to use a laser beam with small wavelength, low energy and a profile with maximum homogenity.

you can consult the website of Silvaco, look where there are examples that can help you.

http://www.silvaco.com/examples/tcad/ 

if you find such a thing, you can take the code section according to your needs (note the name of the file must be changed)

good luck 

Thanks! Of course diamond is not the most simple material to deposit or to pattern, so I continue to be on the lookout for other materials that can more easily be deposited as a smooth thin film.

Dear Cyril,

Any representation has its objectives.

Let us analyse the two figures representing the same data. That is the transistor curves.

The transistor i-v characteristics can be expressed formally by the function:

IC= f( VCE , IB)

From the two port notation of the transistor, the output port parameters are IC and VCE.

IB represents  the  effect of the input port current on the collector current. 

Accordingly, to represent the output transistor characteristics on a two dimensional graph one has to choose VCE as a continuous variable and IB as a discrete variable having with proper steps. It is so that we sample the base current. This is the conventional way where the value of the base current is written on it as a label for the figure. Such transistor iv representation is used to solve graphically the tranistor circuit. We all know the concept of the load line and the DC operating point. so this presentation is characterized by its simplicity and ease of use.

Now it is to be compared by the three dimensional representation of the same transistor curves that you propose.

It is so that you add a third axes to represent the base current and then you have to draw the transistor curve at the new base current in an other plane shifted by the magnitude of the base current. So, there is no need to label the curve. This is the single benefit from the three dimensional representation. Which means that you use a different page to draw an i-v curve.

This new representation will complicate the concept of the graphical solution.

So, the only benefit is  not to label the i-v curves with the base current but with a more complicated solution.

I do not see any advantage from the three dimensional representation of the the output tranistor curves. In the opposite it brings unneeded complications.

This is my opinion on your proposal.

Best regard  

Yes, a pick up coil is the way to go, attached to an oscilloscope.  To calibrate it, you can run an alternating current of known amplitude through a larger coil with a known diameter and number of turns, and then measure the voltage response in your pick up coil (which you would place inside the larger coil with axes parallel).  You can calculate the magnetic field produced by the large coil of known geometry and known alternating current.  Choose a few different alternating current values for the large coil and measure the resulting voltage in the pickup coil each time.  Then you can plot pick up coil voltage vs B field in large coil.  Now you have a calibration curve for the pick up coil.  Now you can measure an alternating  B-field of unknown amplitude.  Remember to orient the pick up coil to obtain the maximum voltage in the unknown field to get the full amplitude of the unknown field.  In summary you need a pick up coil, an oscilloscope with a bandwidth of at least 126 kHz, a source of alternating current, a way to measure the alternating current, and a large coil to generate a test field.  Good luck!

I don't see what you mean by change of gravitational mass because of magnetic fields (at least not without utterly unobtainable magnetar like magnetic fields), but I can certainly see how even minute magnetisation effects in a strong magnetic field (by earth standards) could provide additional torques on a suspended test mass that would make Eotvos type experiments even more difficult than they are without a magnetic field. I would be interested to know how you think strong magnetic fields can validate the Eotvos experiment.

Perhaps this link could be helpful: http://home2.fvcc.edu/~dhicketh/DiffEqns/Spring11projects/Ben_Lynch_Gavin_Lommatsch/DiffEqProject/DiffEqProjectGavinBen.pdf

The inter-atomic potential allows to calculate the dynamic matrix . From its diagonalization you can get the phonon dispersion. I think what you have to do is to model. You have to make assumptions whether there are only nearest neighbor interaction or next nearest neighbor interactions etc. Based on a model with free parameters (spring constants) you can try to reproduce the dispersion relation. This is similar to x-ray analysis where there is no straight forward possibility to solve the inverse problem. You need a model, and make a best fit with it. If the data are reproduced you get your force constants from the fit. If the data can't be reproduced you need to refine your model in your case by allow higher order interaction. 

A flat tip nano indenter will help with indirect estimation of Young's modulus and has high reproduciblility, Also, most of the instruments come equipped with a PID controlled temperature chamber to measure temperature dependency of properties.

Further, if you have randomly shaped nano-particles I would personally suggest focused ion-beam etching to properly shape the contact area prior to measurements.

I hope it helps. 

For example if we have a spin -1 system, then we know that its 3 components in a stern gerlach exptt will be +-1 and 0. Now I am interested in measuring S^2 for the same system, and I know it will have only two components +1 and 0. I hope its clear now.

As a complement to above (clarifying) answer by V. Alejandro Suárez Toriello, I just want to add my two cents, by mentioning that WO₃ dissolves in hot NH₄OH (aq).

You can browse the web site of phywe company, here you are

while you define the properties of the Particle Source select "Fixed" in "Tracking Emission Model", then select "Edit" and define the properties of the Model. (CST Particle Studio 2011).

Try to centrifuge the colloid with 5000-6000 RPM for !5 mins. Pellet is formed. That can be used for SEM 

What about Brewster's Angle? The intensity of the light reflected in the dielectric surface should be =0 for p-polarized incident light.

The main issue here is the fact, that signal generator may not behave as expected, when you will connect it to a current source (which a solar cell is).  You may check thet in specification, or even better - send a query to Agilent tech support. In likely case that it cannot sink current opposite to driven voltage you will need to look for equipment  called source meter.  If you look for a bargain price, you may check

 http://mkto-sj070048.com/VoPR000sdk0H200WUrh1f80

for genuine refurbished keithley equipment.

If you plot the spectrum as a function of 1/wavelength, you may find that the peaks are more eqidistant with similar width.  Look at the équations describing interférence and you will see the dépendance on 1/wavelwngth. 

Thank you sir. i will follow these papers.

Trying to put some order in the answers.

The answer depends on the value of the "vacuum" yo do consider.

- Poor vacuum = a small fraction of the atmospheric pressure. The applied voltage creates a real plasma made out of ions from the residual gas and electrons.

- UHV - Ultra High Vacuum = the value of vacuum in space, ~1 atom/m³. A plasma can be created from matter ripped off from the electrodes.

- The third answer is about the creation of particles in vacuum from vacuum. Ultra-high electric fields can create particles in vacuum but this takes place at the ultra-high energy levels one finds in stellar reactions. Sumit Mishra, this part is related to the high energies generated with ultra-short light pulses I wrote about in the answer to one of your other questions.

The conquest of knowledge has not limit, we must go everywhere we can go, explore every corner of the Universe.

I agree, this answer is too general. Here are some more practical arguments.

- If you want to picture a moving car with a camera you need to expose the film no more than about 1/100th of a second for the picture to be sharp. If you would like to picture the flying bullet of a firearm you would live the camera open in a dark room and shine the bullet with a nanosecond flash of light at the time it passes in front of the camera. When exploring the fastest dynamics of electrons in semiconductors you need femtosecond light pulses, and you want to explore the fastest dynamics of electrons because you want computer to run ever faster.

- This argument does not apply to attosecond light pulses because even the light objects like electrons do move too slowly at an attosecond time scale. The second strong argument favouring short pulses goes as follows. If you can put as much energy in an attosecond light pulse than in a nanosecond light pulse then the peak power of the attosecond pulse is a billion times larger than the peak power of the nanosecond pulse. When we will be able to produce pulses with peak powers larger than 10²⁰ W/cm² then we will be able to observe the interaction of two visible photons. In the mean time we will explore the field of photo induced nuclear reactions.

Theoretical model of laser ablation (at least one of them) is called two temperature model. And it speaks separately about temperature (kinetic energy) of electrons and of nucleis. Basically it says the following: First electrons absorb the optical energy, and either in a ladder like manner (for longer pulses) or by direct multi-photon process (for shorter ones) are getting out of bound states to continuum.  Now two things can happen to the electron:

1. It will collide with a nuclei ant transfer its energy to phonons (thermalization)

After many collisions, nuclei will gain enough energy to escape the bulk

2. Electrons are gaining lots and lots of energy and leave the material (kind of multi-photon photoelectric effect). Nuclei stay cool. But after enough electrons have left, the nuclei remain unbound, and "fly away" due to room temperature energy.

The second mechanism, obviously affects much less area. In fact, being naturally multi-photon, the ablated area is proportional to intensity in the optical spot size in high power, effectively making the "hole" smaller. 

This second type of ablation is claimed to be used in medical devices for ophthalmology, where the size of the perforation is most critical. 

As far as I remember it was nice series of experiments shown by P. Bucksbaum at Stanford, using ultra-fast femtosecond ablation followed by ultra-short x-ray diffraction, where they have verified the second mechanism. I would check about years 2005-2009, but not sure exactly.  

Here is more recent paper, that looks relevant:

Optics Express, Vol. 20, Issue 28, pp. 29329-29337 (2012)

Hello Sumit (and others) --

(I posted this answer in the other thread before seeing you had created a new one. Here I have copied the answer for the benefit of anyone else following the conversation.)

People use several different kinds of lasers for producing the femtosecond pulse durations needed to drive high harmonic generation. This is actually its own field of research: in addition to ubiquitous Ti:sapphire-based systems, many researchers have achieved truly remarkable results relevant to attoscience with laser architectures based on optical parametric chirped-pulse amplification (OPCPA) or chirped-pulse amplification (CPA) in fibers and other solid-state gain media. Of course, each type of laser has its advantages (e.g. repetition rate, pulse energy, wavelength) that may make it more suitable for certain applications over others.

Speaking specifically of Ti:sapphire lasers (which you had asked about previously), most current setups used for generating isolated attosecond pulses involve a femtosecond oscillator, a pulse stretcher, the amplifier itself (which may consist of regenerative or multi-pass configurations, or both), and a pulse compressor. Because of gain-narrowing due to amplification of the pulse energy from the ~nJ to the ~mJ level, the pulse duration is usually limited to >25 fs, which is too long for generating isolated attosecond pulses with most common gating methods. (Because it relates to my own research, I will mention that an exception to this rule of thumb is double optical gating (along with its variants), which allows isolated attosecond pulse generation with pulses directly from the amplifier and compressor. This method can also work without facing the challenges of carrier-envelope phase (CEP) stabilization, which is required for most few-cycle gating methods like amplitude gating and ionization gating.)

Because of the long pulse durations after the compressor, most typical setups use a hollow-core fiber or filamentation tube to generate an ultrabroadband spectrum (e.g. several hundred nm) through self-phase modulation (SPM). This spectrum can be compressed using ultrabroadband chirped mirrors down to pulse durations as short as <5 fs. After this, the pulses are ready for gated high harmonic generation, which typically involves a focusing element, a gas jet or gas cell, and a way to separate the driving infrared (femtosecond) pulses from the resulting extreme ultraviolet (attosecond) pulses. The filtering and other specifics of the setup will depend on the type of gating that is chosen.

I hope this generally answers the question you had in mind.

Best,

~Eric (Institute for the Frontier of Attosecond Science and Technology, UCF)