Measurement of the 24Mg(p, t)22Mg reaction for the states near the 21Na + p threshold
ABSTRACT Differential cross-sections of the 24Mg(p, t)22Mg reaction were measured at 34.68 MeV for the states near the proton threshold at 5.502 MeV in 22Mg. Among them, the new states at 5.962, 6.046, 6.246 and 6.323 MeV, which were reported previously, have been confirmed.
Angular distributions for these states were analyzed by distorted-wave Born-approximation calculations to deduce the spins
and parities. The angular distribution for the 5.714 MeV state, which is considered to be most crucial for the stellar reaction
21Na(p, γ)22Mg, has been found to be consistent with J
π = 2+ assignment. The 6.046 MeV state is newly assigned to have J
π = 0+, and the 5.962 MeV state is tentatively assigned to have J
π = (1-). These two states will also play an important role for 22Mg production in novae.
Eur. Phys. J. A 14, 275–278 (2002)
PHYSICAL JOURNAL A
c ? Societ` a Italiana di Fisica
Measurement of the24Mg(p,t)22Mg reaction for the states near
the21Na + p threshold
S. Michimasa1,a, S. Kubono1, S.H. Park2, T. Teranishi1, Y. Yanagisawa3, N. Imai4, Zs. F¨ ul¨ op5, X. Liu1,
T. Minemura3, C.C. Yun1, J.M. D’Auria6, and K.P. Jackson7
1Center for Nuclear Study (CNS), University of Tokyo, RIKEN Campus, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
2School of Physics, Seoul National University, Seoul 151-747, Republic of Korea
3RIKEN (The Institute of Physical and Chemical Research), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
4Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan
5Institute of Nuclear Research of the Hungarian Academy of Sciences, H-4001 Debrecen, P.O. Box 51, Hungary
6Department of Chemistry, Simon Fraser University, V5A 1S6 Burnaby, Canada
7TRIUMF, V6T 2A3 Vancouver, Canada
Received: 7 March 2002
Communicated by D. Guerreau
Abstract. Differential cross-sections of the24Mg(p,t)22Mg reaction were measured at 34.68 MeV for the
states near the proton threshold at 5.502 MeV in22Mg. Among them, the new states at 5.962, 6.046, 6.246
and 6.323 MeV, which were reported previously, have been confirmed. Angular distributions for these
states were analyzed by distorted-wave Born-approximation calculations to deduce the spins and parities.
The angular distribution for the 5.714 MeV state, which is considered to be most crucial for the stellar
reaction21Na(p,γ)22Mg, has been found to be consistent with Jπ= 2+assignment. The 6.046 MeV state
is newly assigned to have Jπ= 0+, and the 5.962 MeV state is tentatively assigned to have Jπ= (1−).
These two states will also play an important role for22Mg production in novae.
PACS. 21.10.Hw Spin, parity, and isobaric spin – 25.40.Hs Transfer reactions – 26.30.+k Nucleosynthesis
in novae, supernovae and other explosive environments – 27.30.+t 20 ≤ A ≤ 38
The nuclear structure of the unstable nucleus22Mg
near and above the21Na + p threshold at 5.502 MeV has
been of interest because of the importance of the stellar
reaction21Na(p,γ)22Mg [1,2]. In ONeMg novae, the top
temperature is typically T9= 0.3–0.4, which corresponds
to Gamow energy at 280–340 keV above the proton thresh-
old [3,4]. Thus, the excited states at around 5.5–6.0 MeV
would make major contributions to produce22Mg. Several
transfer reactions, the24Mg(p,t) [5,6], the20Ne(3He,nγ)
[7,8], the20Ne(3He,n) [9,10], and the12C(16O,6He) re-
actions , were studied in order to obtain information
on the excited states in22Mg, which can be used for an
estimate of the21Na(p,γ)22Mg reaction rate.
In our previous work, we observed new levels at 5.962,
6.046, 6.246 and 6.314 MeV and precisely determined the
excitation energies of the levels, which are located near
the proton threshold in22Mg, by the24Mg(p,t) reaction
at 37.925 MeV . However, the spins and parities were
not assigned for these states. We extended our study to
confirm the new levels by changing the incident energy and
also measuring at a wider angular range. We measured the
angular distributions for the states of possible importance
for the hydrogen burning, including the new states, and
made spin assignments for the states.
The experiment was performed at the Center for Nu-
clear Study (CNS), University of Tokyo. Differential cross-
sections for the24Mg(p,t)22Mg reaction were measured.
A 34.68 MeV proton beam obtained from the CNS-SF cy-
clotron bombarded a24Mg metallic foil of 358±12 µg/cm2
enriched to 99.9%. The beam current on the target was
monitored by a Faraday cup placed just after the target.
The typical current was about 100 nA. Outgoing parti-
cles were analyzed by a high-resolution magnetic spec-
trograph, PA . The solid angles for tritons were de-
fined by an aperture of 5.0 msr, which was installed at
350 mm downstream from the target position. Along the
focal plane, a detector system was placed, which consisted
of a hybrid-gas counter  and a plastic scintillator with
276The European Physical Journal A
photomultiplier tubes on both sides. The gas counter pro-
vided position information on the focal plane and energy
losses (∆E) of the particles in the counter. The plastic
scintillator gave energies (E) and the timing for time-of-
flight (TOF) measurement from the target to the scin-
tillator. The start time was obtained from the RF signal
of the cyclotron. Particle identification was made using
∆E, E, and TOF for each particle. Energy spectra of
the triton were obtained from the position information
given by the gas counter. Triton spectra near the proton
threshold were obtained at nine angles, 13.0, 20.0, 23.5,
27.0, 34.0, 44.5, 48.0, 55.0, and 62.0 degrees in the lab-
oratory system. Overall energy resolution observed was
about 37.5 keV FWHM for tritons. We also measured an-
gular distributions for the ground state and the first ex-
cited state in22Mg at 10.0–80.0 degrees in 5.0 degrees
steps to check the validity of the distorted-wave Born-
approximation (DWBA) and to determine the optical po-
tential parameters for DWBA analysis.
Excitation energy in22Mg was determined by a mean
value of excitation energies obtained at each measured an-
gle. We can identify reacting target nuclei from kinemat-
ical shifts of triton momenta as a function of the angle.
Thus, measurement at a wide angular range is required for
the distinction of the22Mg peaks from the contamination
peaks. Table 1 summarizes the excitation energies in22Mg
observed in the present experiment together with the re-
sults in ref. . Although the beam energy was changed
from 37.9 MeV to 34.7 MeV, all the states were clearly
observed at the same excitation energies in22Mg. In the
present experiment, triton peaks from the 3.35 MeV state
in10C and from the states at 6.27 MeV, 6.59 MeV and
6.79 MeV in14O were identified as contamination. Since
the contamination peaks were the well-known states in
10C and14O, the yields were estimated by the DWBA
calculations, for which optical potential parameters were
taken from refs. [14,15].
The state at 5.962 MeV was observed again in the
present experiment. Triton momenta from the state, which
was measured at angles from 13 degrees to 62 degrees, were
consistent with the one from24Mg(p,t)22Mg reaction. The
excitation energy obtained is 5.960 MeV in22Mg from the
calibration with an uncertainty of 8 keV. Thus, the new
Table 1. Experimental excitation energies in22Mg. The first
column implies the results in the present experiment, and the
second the ones in ref. . The last column shows the excitation
energies adopted by the present experiment. The energies in
italic characters were used for the energy calibration.
E =6.046 MeV
E =5.962 MeV
E =0.0 MeV, 0 +
24Mg(p,t)22Mg reaction for the ground state and excited states
in22Mg at 6.046 MeV and 5.962 MeV together with the DWBA
calculations. The lines are the calculations for the transferred
angular momenta L denoted.
1. Angular distributions of the tritons from the
state at 5.962 MeV has been confirmed in the present ex-
periment. The doublet states at 6.250 MeV and 6.323 MeV
have also been confirmed here by the same way.
Spin assignments have been made using the DWBA
analysis for the angular distributions, where the anal-
ysis is made with the code TWOFNR . Figures 1
and 2 show the experimental angular distributions for the
24Mg(p,t)22Mg reaction together with the lines predicted
by the DWBA calculations.
As for the optical potential parameters of the initial
and the final channels, we adopted those in ref. , which
roughly reproduce the measured angular distributions for
the ground and the first excited state in22Mg. A Woods-
Saxon form factor with r = 1.25 fm and a = 0.65 fm was
used for the bound-state potential, where the depth was
determined to reproduce the separation energy.
Typical shapes of L = 0 and 2 angular distributions
can be seen in the transitions to the ground state in fig. 1
and to the 2+
oscillation phases of L = 0 and 2 are similar to each other,
the L = 2 distribution has a smooth increase at forward
1state in fig. 2, respectively. Although the
S. Michimasa et al.: Measurement of the24Mg(p,t)22Mg reaction for the states near the21Na + p threshold277
E =5.714 MeV
E =1.246 MeV, 2 +
24Mg(p,t)22Mg reaction for the excited states in
1.246 MeV and 5.714 MeV together with the DWBA calcula-
tions. The lines are the calculations for the transferred angular
momenta L denoted.
2.Angular distributions of the tritons from the
angles, whereas the L = 0 distribution has a distinct os-
cillations and a sharp increase near zero degree.
The 5.714 MeV and 6.046 MeV states in22Mg are con-
sidered to play an important role in the21Na(p,γ)22Mg
reaction during novae nucleosynthesis. The 2+state is
known to be located at around 5.7 MeV from the (3He,n)
 and the (3He,nγ)  reaction studies. The angular dis-
tribution for the 5.714 MeV state is similar to the data for
(p,t) reaction, and the L = 2 DWBA curve rather than
the L = 0 curve (see fig. 2). Therefore, the present re-
sult supports by the24Mg(p,t)22Mg reaction the previous
assignment that 5.714 MeV state in22Mg has 2+.
Previously, only one state of Jπ= 0+state was known
at around 6.0 MeV from the (p,t) reaction  at 41.9 MeV.
Since the 6.046 MeV state in the present experiment is
more strongly excited than the 5.962 MeV state, roughly
by a factor of ten, the 6.046 MeV state should be the one
observed in ref. . In fact, the angular distribution for
the 6.046 MeV state is quite similar to the one for the
ground state and reasonably well explained by the L = 0
DWBA calculation. Thus, Jπ= 0+is assigned here for
the 6.046 MeV state.
The 5.962 MeV state could be important also for22Mg
production in ONeMg novae as it is located in the mid-
dle of the Gamow peak at T9= 0.4, although nothing is
known for the spin and parity of this state. The measured
differential cross-sections for the state was about 0.1–1
µb/sr. Thus, a high energy resolution was required to dis-
tinguish a state nearby, including contaminant peaks. The
angular distribution for the state could be explained ei-
ther by L = 0 or 1, although the fit is not so good. In
the mirror nucleus,22Ne, there is a 1−state at 6.69 MeV,
1state, which was measured for the first time in the
Table 2. Spin and parity assignments for the states in22Mg
near and above the proton threshold in the present experiment
together with previous experimental results.
Ex Alford 
L = 2
}L = 0
and no other 0+state around 6.0 MeV. All other states
in this energy region in22Ne have corresponding states in
22Mg. Therefore, the 5.962 MeV state is reasonable to be
assigned to have Jπ= 1−.
The present spin assignments for the excited states, are
summarized in table 2. The 5.837 MeV state was observed
only in ref. . There was no indication in the present ex-
periment. The last column shows spin and parity assign-
ments adopted here.
In summary, the new states at 5.962 and 6.046 MeV
in22Mg have been confirmed in the present experiment.
New spin parity assignments have been also made for the
states just above the proton threshold. However, some of
the assignments are still tentative, and thus further work
is awaited experimentally for spin assignment.
The new states established in the present experiment
could be important for22Mg production in novae. The
states at 5.714, 5.813, 5.962 and 6.046 MeV are recom-
mended to be included in the nova model calculations.
The 5.962 MeV(1−) state should be a p-wave resonance
in22Mg and be effective in the vicinity of the top temper-
ature of ONeMg novae. The reaction rate including a 1−
state was discussed in ref. , although the spin assign-
ment there was only an assumption. The contribution of
the 5.96 MeV state is estimated to be about 10% of the
total reaction rate at T9= 0.4. Further information on the
5.96 MeV state, especially the resonance strength, is defi-
nitely required for a precise estimate of the21Na(p,γ)22Mg
This work is partly supported by a Grant-in-Aid for Science
Research from the Japanese Ministry of Education, Culture,
Sports, and Technology under the contract no. 13440071.
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