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UNCORRECTED PROOF
)=NH>86)=NH>8HD;DC9:CH:9&6II:G MMM MMMM MMMMMM
DCI:CIHA>HIH6K6>A67A:6I,8>:C8:>G:8I
)=NH>86)=NH>8HD;DC9:CH:9&6II:G
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%D86A HIGJ8IJG: 6C9 @>C:I>8H D; E6G6B6<C:I>8 9:;:8IH >C9J8:9 7N γ>GG69>6I>DC D; I=:
:G7>JB 9DE:9 < 6 :, <A6HH:H
$DC8=>IH 6 ,=6C>C66 /( 2J@=NB8=J@ 6 //!6AN6C7∗ ,/ $G6HCDKN9 6 ((%:7:98
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6V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine, Kyiv, Ukraine
7Eastern European National University Named By Lesya Ukrainka, Lutsk, Ukraine
8National University for Water Economy and Nature Management, Rivne, Ukraine
9Lutsk National Technical University, Lutsk, Ukraine
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Keywords
=6A8D<:C>9: <A6HH
G7>JB
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,-+-
:;:8IH >C9J8:9 7N γ>GG69>6I>DC >C G;G:: 6C9 G9DE:9 <A6HH:H < 6 :, L:G: HIJ9>:9 JH>C< I=: +6B6C
6C9 )+ HE:8IGDH8DE>:H "I >H H=DLC I=6I γ>GG69>6I>DC 86JH:H 6C >C8G:6H: >C I=: >CI:CH>IN D; +6B6C 76C9H G:
A6I:9 L>I= ;DGB6I>DC D; , : :,HIGJ8IJG6A <GDJEH JG>C< I=: ADLI:BE:G6IJG: 6CC:6A>C< 6I I:BE:G6IJG:H D;
– R I=: 8DC8:CIG6I>DC 'HD; γ>C9J8:9 E6G6B6<C:I>8 8:CIG:H ) =6K>C< I=: 6M>6A HNBB:IGN D; I=: <I:C
HDG L>I= <O 6C9 <M <N >H 7:>C< HIGDC<AN G:9J8:9 6C9 I=: HNBB:IGN D; I=: :CK>GDCB:CI
D; I=:H: 8:CIG:H 7:8DB:H ADL:G ,J7H:FJ:CI HIDG6<: D; 6CC:6A:9 H6BEA:H >C I=: 6>G ;DG 67DJI 96NH A:69H ID 6
<G69J6A G:HIDG6I>DC D; I=: 'H8DC8:CIG6I>DC -=: @>C:I>8H D; I=:H: EGD8:HH:H >H 9:H8G>7:9 I6@>C< >CID 688DJCI 7DI=
I=: =><= BD7>A>IN D; HJA;JG K686C8N 6C9 I=: ADC<I>B: G:A6M6I>DC D; I=: <A6HH HIGJ8IJG: 8DGG:A6I>DC 7:IL::C I=:
>CI:CH>IN D; 8B−+6B6C 76C9 7:ADC<>C< ID I=: , : 6 6 :,8DBEA:M 6C9 ) 8=6G68I:G>HI>8H >H 9>H
8JHH:9
1. Introduction
-=: JC>FJ: ;:6IJG: D; 8=6A8D<:C>9: <A6HH:H = 9DE:9 L>I= :G
7>JB >H I=: 8DB7>C6I>DC D; >CI:CH: E=DIDAJB>C:H8:C8: )% L>I= =><=
IG6CHE6G:C8N >C I=: K>H>7A: 6C9 C:6G>C;G6G:9 G:<>DCH 45 L=>8= B6@:H
I=:B EGDB>H>C< ;DG JH: >C I:A:8DBBJC>86I>DC 9:K>8:H >C E6GI>8JA6G >C
HE68: -=: G69>6I>DC HI67>A>IN D; I=:H: B6I:G>6AH >H >BEDGI6CI 7:86JH: ;DG
B6I>DC D; 9:;:8IH 7N γ>GG69>6I>DC 6;;:8IH I=: HIGJ8IJG: 6C9 )% EGDE:GI>:H
D; = +:6AAN >I L6H ;DJC9 >C B6CN HIJ9>:H I=6I G69>6I>DC>C9J8:9 9:
;:8IH D88JG >C I=: 8GNHI6AA>C: 6C9 <A6HH 8=6A8D<:C>9:H JC9:G I=: 68I>DC
D; I=: γG6NH 4–5 -=: AD86A HIGJ8IJG: >H IG6CH;DGB:9 45 699>I>DC6A
G69>6I>DC>C9J8:9 67HDGEI>DC 76C9H B6N D88JG >C I=: DEI>86A 67HDGE
I>DC HE:8IG6 45 6C9 CDCA>C:6G E>:ODDEI>86A 6C9 )% EGDE:GI>:H 8=6C<:
4–5 .C9:G A6G<: 9DH:H D; G69>6I>DC I=: 76C9 <6E 9:8G:6H:H 45
-=: 67>A>IN D; G69>6I>DC ID 6;;:8I DEI>86A EGDE:GI>:H D; HJ8= H:B>8DC9J8
IDGH 86C 7: JH:9 ;DG 9:H><C D; 8DCI68IA:HH H:CHDGH (C I=: DI=:G =6C9
I=: IG6CHE6G:C8N >C I=: K>H>7A: 6C9 >C;G6G:9 HE:8IG6A 76C9H I=: 67>A>IN D;
= ID IG6CHB>HH>DC D; DEI>86A 96I6 6H L:AA 6H 6 G:A6I>K:AN A6G<: >C9:M
D; G:;G68I>DC 6C9 I=: FJ6CIJB N>:A9 D; )% 6AADLH I=:>G JH6<: 6H 68I>K:
B:9>6 >C A6H:G I:8=CDAD<N 45 DEI>86A I=:GBDB:I:GH 45 A><=I 8DC
K:GI:GH 45 6C9 X7:G DEI>8H 45
"I >H E6GI>8JA6GAN >BEDGI6CI ID >CK:HI><6I: I=: D88JGG:C8: 6C9 IG6CH
;DGB6I>DC 9NC6B>8H D; I=: 9:;:8I HJ7HNHI:B 6;I:G γ>GG69>6I>DC >C 8=6A8D
<:C>9: <A6HH:H 9DE:9 L>I= A6CI=6C>9:H G )G J '9 :I8 L=>8= 8DC
HI>IJI: 6 76H>H ;DG I=: BD9:GC DEID:A:8IGDC>8 9:K>8:H -=: :;;:8I D; γ>G
G69>6I>DC DC I=: IG6CH;DGB6I>DC D; I=: 9:;:8I HJ7HNHI:B >C = 6C
C:6A:9 6I ADL I:BE:G6IJG:H >H HD ;6G CDI HJ;X8>:CIAN HIJ9>:9 -=: B:I=D9
D; B6<C:I>8 G:HDC6C8: >H I=: BDHI HJ>I67A: ;DG >CK:HI><6I>DCH >C I=>H
X:A9 88DG9>C< ID +:; 45 I=: 9:;:8I HJ7HNHI:B >C I=: < 6 :,
<A6HH:H 9>G:8IAN 6;;:8IH I=: DEI>86A EGDE:GI>:H G 8AJHI:G>C< 6C9 :K:CIJ
6AAN I=: )A EGDE:GI>:H H L>AA 7: H=DLC >C I=: EG:H:CI LDG@ I=: HIJ9>:9
=:G: E6G6B6<C:I>8 9:;:8IH =6K: 6 ADL 9>H>CI:<G6I>DC I=G:H=DA9 6C9 86C
7: IG6CH;DGB:9 ID I=: CDCB6<C:I>8 HI6I: 6I I=: ADL I:BE:G6IJG: 6CC:6A
>C< -=>H IG6CH;DGB6I>DC >H G:K:GH>7A: 6I GDDB I:BE:G6IJG: -=: HIJ9N D;
I=:H: EGD8:HH:H 9NC6B>8H L>AA H=:9 A><=I DC I=: 9:;:8I C6IJG: I=:>G E6G
I>8>E6I>DC >C I=: 9:;:8I 8AJHI:G>C< 6C9 EG:9>8I>DC D; DEI>86A EGDE:GI>:H >C
I=: HNHI:B JC9:G γ >GG69>6I>DC
AI=DJ<= I=: :,<A6HH =6H 7::C HIJ9>:9 ;DG 6 ADC< I>B: C:L EGDE
:GI>:H D; HDA>9 :A:8IGDANI:H 6G: ;DGB:9 >; H>AK:G >H 699:9 6H I=: < 6IDBH
=6K: 6 =><= BD7>A>IN >C = 45 -=>H XC9>C< 86JH:9 B6CN 6EEA>86
I>DCH A>@: H:CHDGH 76II:G>:H 6C9 B:BDGN 9:K>8:H 45 -=: H>AK:G
9>;;JH>DC 86C 7: 688:A:G6I:9 7N I=: G69>6I>DC 6C9 6H 6 G:HJAI 6 H><C>;>
∗DGG:HEDC9>C< 6JI=DG
E-mail address: =6AN6CKJ@GC:I // !6AN6C
=IIEH9D>DG<?E=NH7
+:8:>K:9 ,:EI:B7:G +:8:>K:9>CG:K>H:9;DGB #6CJ6GN 88:EI:9 #6CJ6GN
K6>A67A:DCA>C: MMM
S
UNCORRECTED PROOF
A.A. Konchits et al. Physica B: Physics of Condensed Matter xxx (xxxx) xxx-xxx
86CI 8=6C<: >C I=: :A:8IG>86A EGDE:GI>:H D; I=: =DHI>C< <A6HH K:C
6I < >CIGD9J8:9 >C I=: 8=6A8D<:C>9: B6IG>M 86JH:H I=: 8=6C<:
D; I=: = 8DC9J8I>K>IN 7N 67DJI DC: DG9:G D; B6<C>IJ9: 45 H 6 G:
HJAI D; I=: G69>6I>DC >C9J8:9 :;;:8IH >C I=: = I=: G:B6G@67A: < 9>;;J
H>DC 6C9 I=: <GDLI= D; <8DCI6>C>C< 8AJHI:GH 86C D88JG -=: 699>C< D; 6
HB6AA ;G68I>DC D; 6 ID I=: <A6HH 6AADLH I=: :G7>JB >DCH ID 7: JC>;DGBAN
9>HIG>7JI:9 I=GDJ<=DJI I=: KDAJB: D; I=: B6IG>M 45 -=>H >H 9J: ID I=:
;68I I=6I I=: IG>K6A:CI G 6C9 6 86I>DCH 6G: G:EA68:67A: >C I=: 76H:
<A6HH:H 45
H HIJ9>:9 >C 9:I6>A >C +:;H 45 I=: HIGJ8IJG: D; I=: :,
<A6HH >H I=: 76H: ;DG < 6 :, <A6HH:H >CK:HI><6I:9 >C I=>H LDG@
"I >H 9:H8G>7:9 7N I=: 9>HDG9:G:9 C:I D; I:IG6=:9GDCH 45 -=: DEI>86A
EGDE:GI>:H D; < 6 :, <A6HH:H L:G: HIJ9>:9 >C +:;H 4–5 6C9
6AHD >C +:;H 45 L=:G: I=: H6B: H6BEA:H L:G: JH:9
"I L6H H=DLC >C +:; 45 I=6I HJ8= H6BEA:H :;;:8I>K:AN AJB>C:H8:C8:
>C I=: K>H>7A: 6C9 C:6G>C;G6G:9 G:<>DCH 6C9 I=: G69>6I>DC :;X8>:C8N 6C9
G69>6I>DC G:H>HI6C8: D; I=: <A6HH H><C>;>86CIAN 9:E:C9 DC I=: :G7>JB 8DC
I:CI
"C I=>H E6E:G I=: AD86A HIGJ8IJG: D; γ>GG69>6I:9 <A6HH:H 6C9 I=: @>
C:I>8H D; E6G6B6<C:I>8 9:;:8IH >C 8DC9>I>DCH D; I=: ADL I:BE:G6IJG: 6C
C:6A>C< – ]V L:G: >CK:HI><6I:9 JH>C< +6B6C HE:8IGDH8DEN 6C9
:A:8IGDC E6G6B6<C:I>8 G:HDC6C8: )+ -=: H6BEA:H D; I=: H6B: INE:H
6H >C +:; 45 C6B:AN I=: :G7>JB;G:: H6BEA: < 6 :, HD 6H
H6BEA:H 6C9 L>I= 6 8DC8:CIG6I>DC D; :G7>JB D; 6C9 6I
G:HE:8I>K:AN L:G: >CK:HI><6I:9 -=: >GG69>6I>DC D; <A6HH:H ;GDB I=: D
HDJG8: L6H E:G;DGB:9 >C I=: 6>G 6I GDDB I:BE:G6IJG: AA I=: H6BEA:H
L:G: γ>GG69>6I:9 L>I= 6 9DH: D; N -=: B:6C :C:G<N D; γG6NH
L6H 8ADH: ID &:/
)+ B:6HJG:B:CIH L:G: 86GG>:9 DJI JH>C< 6 8B HE:8IGDB:I:G “+6
9>DE6C”,1 -D 9:I:GB>C: I=: 8DC8:CIG6I>DC D; E6G6B6<C:I>8
8:CIG:H ) 6 G:;:G:C8: H6BEA: &<( G L>I= I=: CJB7:G D; HE>CH
'G ⋅ L6H JH:9 -=: +6B6C HE:8IG6 L:G: :M8>I:9 7N I=:
HDA>9 HI6I: A6H:G L>I= I=: L6K:A:C<I= D; CB 6C9 68FJ>G:9 JH>C< H>C
<A: HI6<: BDCD8=GDB6IDG :FJ>EE:9 L>I= C9DG 9:I:8IDG
2. Results and discussion
2.1. Raman spectroscopy characterization of glasses
-=: +6B6C HE:8IGDH8DEN >H 6C :;;:8I>K: B:I=D9 ;DG 6C6ANO>C< I=:
HIGJ8IJG6A DG9:G>C< >C I=: :,,: INE: <A6HH:H >C8AJ9>C< I=: :;;:8I D;
K6G>DJH >BEJG>I>:H 6C9 I:8=CDAD<>86A IG:6IB:CIH DC I=:>G HIGJ8IJG: &6C
>;:HI6I>DCH D; I=: DH8>AA6I>DCH 8DGG:HEDC9>C< ID 8:GI6>C HIGJ8IJG6A JC>IH
>C I=: HE:8IG6 D; I=: 76C9H 8=6C<: >C I=:>G >CI:CH>IN =6A; L>9I= 6C9 >C
;G:FJ:C8N EDH>I>DC EGDK>9: ;DG I=: 8DCIGDA D; I=: EGD8:HH:H D; HNCI=:
H>H 9DE>C< I:8=CDAD<>86A IG:6IB:CIH 6C9 :MI:GC6A >CYJ:C8: -=: +6B6C
HE:8IG6 D; G;G:: 6C9 G9DE:9 <A6HH H6BEA:H CDC>GG69>6I:9 6C9 γ>GG6
9>6I:9 L>I= 6 9DH: D; N 6G: H=DLC >C >< -=: 6C6ANH>H D; +6
B6C HE:8IG6 L6H E:G;DGB:9 DC I=: 76H>H D; 6 9>HDG9:G:9 <G>9 BD9:A 45
L=>8= 8DCH>HIH D; 8DGC:G H=6G>C< :, I:IG6=:9GDCH 6C9 :9<:H=6G>C<
:, I:IG6=:9GDCH
-=: BDHI >CI:CH>K: 76C9 L>I= I=: ;G:FJ:C8N D; 8B 8DGG:HEDC9H
ID HNBB:IG>8 HIG:I8=>C< K>7G6I>DCH D; I=: HNBB:IGN D; 8DGC:GH=6G>C<
: 6,I:IG6=:9GDCH L=>8= >H I=: B6>C HIGJ8IJG6A JC>I >C I=: : 6,
<A6HH:H 45 88DG9>C< ID I=: 8DBEDC:CI 8DBEDH>I>DC D; I=: HIJ9>:9
8DBEDJC9 I=: 6, I:IG6=:9GDCH 6G: 6EEGDM>B6I:AN 7N DG9:GH D;
B6<C>IJ9: HB6AA:G "C 699>I>DC I=: :A:B:CIH D; : 6C9 6 =6K: 8ADH:
B6HH:H 6C9 ;DG I=>H G:6HDC I=: ;G:FJ:C8>:H D; I=: 8DGG:HEDC9>C< 76C9H
L=>8= 6G: B6C>;:HI:9 >C I=: +6B6C HE:8IG6 6G: FJ>I: 8ADH: "I B:6CH I=6I
>I >H >BEDHH>7A: ID H:E6G6I: I=: 76C9H >C I=: HE:8IGJB G:HEDCH>7A: ;DG
6, K>7G6I>DCH
-=: 76C9 L>I= 6 ;G:FJ:C8N D; 8B−86AA:9 I=: 876C9 >H 6H
H><C:9 ID I=: K>7G6I>DC6A BD9: D; I=: :9<:H=6G>C< :,I:IG6=:9GDCH
45 -=: BDHI 8DCIGDK:GH>6A ID96N >H I=: C6IJG: D; I=: DH8>AA6I>C<
BD9: L=>8= 86JH:H 6 76C9 L>I= 6 ;G:FJ:C8N D; Q 8B−>C I=: +6
Fig. 1. +6B6C HE:8IG6 CDGB6A>O:9 ID I=: >CI:CH>IN D; I=: 76C9 8B 6 CDC>GG69>6I:9 H6BEA:H 6C9 L>I= 9>;;:G:CI E:G8:CI6<:H D; :G7>JB 6C9 6I 7 H6BEA:
7:;DG: 6C9 6;I:G >GG69>6I>DC 8 H6BEA: 7:;DG: 6C9 6;I:G >GG69>6I>DC 9 H6BEA: 7:;DG: 6C9 6;I:G >GG69>6I>DC 6H L:AA 6H 6;I:G 6CC:6A>C< -=: >CH:I ID >< H=DLH I=: HE:8IGJB D; I=:
>C>I>6A H6BEA: 6C9 >IH 9:8DBEDH>I>DC >CID 8DBEDC:CIH
UNCORRECTED PROOF
A.A. Konchits et al. Physica B: Physics of Condensed Matter xxx (xxxx) xxx-xxx
B6C HE:8IGJB .CA>@: I=: DI=:GH I=>H 76C9 >H CDI 8A:6GAN B6C>;:HI:9
>C I=: HE:8IGJB CDI K>H>7A: >C I=: B6M>BJB D; I=: 76C9 !DL:K:G >I
>H 9:I:8I:9 DCAN 6H 6 G:HJAI D; I=: :ME6CH>DC D; I=: 8DBEA:M HE:8IGJB
DC H:E6G6I: 8DBEDC:CIH >< 6 >CH:GI 88DG9>C< ID +:; 45 I=:
HJ776C9 L>I= 6 B6M>BJB 6I 8B−>H 86JH:9 7N K>7G6I>DCH D; I=:
8DGC:GH=6G:9 <GDJEH :, "C 6CDI=:G LDG@ 45 I=: 76C9 L>I= 6
;G:FJ:C8N D; Q 8B−>H 6HHD8>6I:9 L>I= I=: EG:H:C8: D; “9:;:8I>K:”
B:B7:G:9 G>C< 8AJHI:GH >C I=: HIGJ8IJG: D; :,<A6HH
7GD69 76C9 L>I= 6 ;G:FJ:C8N D; Q 8B−>H 6HHD8>6I:9 L>I= YJ8
IJ6I>DCH D; ILD I:IG6=:9GDCH L=>8= 6G: 8DCC:8I:9 7N K:GI>8:H I=GDJ<= 6
7G>9<: 6C 6IDB D; HJA;JG >C , :, :,45 88DG9>C< ID +:; 45
I=: 8DCIG>7JI>DC ID I=>H 76C9 86C 6AHD 7: <>K:C 7N I=: DH8>AA6I>DCH D;
H=DGI ,–, 8=6>CH 7:IL::C :,I:IG6=:9GDCH
76C9 L>I= 6 ;G:FJ:C8N D; Q 8B−>H 6HHD8>6I:9 L>I= YJ8IJ6
I>DCH D; I=: HIGJ8IJG6A JC>IH D; , : 6 6 :,45 H 86C 7: H::C
;GDB >< 6 6C >C8G:6H: D; CDC8AJHI:G:9 :G7>JB 8DCI:CI >C I=: <A6HH
A:69H ID 6C >C8G:6H: >C I=: >CI:CH>IN D; DCAN ILD 76C9H L>I= ;G:FJ:C
8>:H D; 6C9 8B−6I I=:>G 8DCHI6CI L>9I= ,>B>A6G 8=6C<:H D8
8JG 6AHD L>I= I=: γ>GG69>6I>DC H 6 G:HJAI I=: γ>GG69>6I>DC A:69H ID
I=: ;DGB6I>DC D; , : :,HIGJ8IJG6A JC>IH 6C9 8DGC:GH=6G:9 <GDJEH
:, (C I=: DI=:G =6C9 I=>H ;68I :K>9:C8:H I=: 9:HIGJ8I>DC D; DI=:G
7DC9 INE:H B:CI>DC:9 67DK: -=: >CI:CH>IN D; I=: 76C9 L>I= 6 ;G:
FJ:C8N D; 8B−6I I=: γ>GG69>6I>DC >C8G:6H:H 9:HE>I: I=: ;68I I=6I
I=: 7>C9>C< :C:G<N : : :/ >H I=: HB6AA:HI >C 8DBE6G>HDC L>I=
:, :/ 6C9 ,, :/ "C I=>H G:A6I>DC >I >H :ME:8I:9 I=6I
I=: CJB7:G D; , : :,HIGJ8IJG6A JC>IH L>AA 9:8G:6H: >C I=: γ>GG6
9>6I>DC EGD8:HH !DL:K:G 6C6ANO>C< +6B6C HE:8IG6 >I >H C:8:HH6GN ID
I6@: >CID 688DJCI I=: ;68I I=6I I=: >CI:CH>IN D; I=: 76C9 L>I= 6 ;G:
FJ:C8N D; 8B−H><C>;>86CIAN >C8G:6H:H L>I= γ>GG69>6I>DC DCAN >C
I=: <A6HH:H 9DE:9 L>I= H>AK:G 46C955 -=: A6II:G B6N 7: 9J:
ID I=: ;68I I=6I 9JG>C< I=: γ>GG69>6I>DC I=: HJA;JG 96C<A>C< 7DC9H 6G:
;DGB:9 L=:G:6H I=: >CI:CH>K: < 9>;;JH>DC HJEEDGIH ;DGB6I>DC D; <,
6C9 < :,8DBEDJC9H HD I=6I I=: G6I>D D; I=: : ID , 6IDBH CJB
7:G >C I=: =DHI>C< 768@7DC: >C8G:6H:H C 699>I>DC6A ADLI:BE:G6IJG:
6CC:6A>C< R D; I=: γ>GG69>6I:9 H6BEA:H >C K68JJB L>I= 6 HJ7H:
FJ:CI =DA9>C< >C I=: 6>G ;DG = 9D:H CDI EG68I>86AAN 8=6C<: I=: >CI:C
H>IN G6I>D 7:IL::C I=: 76C9H D; 8B−6C9 8B− I I=: H6B:
I>B: I=: >CI:CH>IN G6I>D 7:IL::C I=: 76C9H D; 8B−6C9 8B−
9:8G:6H:H H:: I=: HE:8IGJB D; I=: 6CC:6A:9 6C9 γ>GG69>6I:9 H6BEA:
>C >< 9
2.2. Kinetics of γ-induced paramagnetic defects during low-temperature
annealing
-=: )+ H><C6AH L:G: CDI 9:I:8I:9 >C I=: CDC>GG69>6I:9 H6BEA:H >:
I=: 8DC8:CIG6I>DC D; E6G6B6<C:I>8 9:;:8IH 'H>H HB6AA:G I=6C I=: G:<>H
IG6I>DC I=G:H=DA9 -=: )+ HE:8IG6 ;DG γ>GG69>6I:9 L>I= 9DH: N
H6BEA:H 7:;DG: 6CC:6A>C< 6G: <>K:C >C ><
=6G68I:G>HI>8 E6G6B:I:GH D; E6G6B6<C:I>8 8:CIG:H ;DGB>C< HE:8IG6 >C
>< 9D CDI 9>;;:G ;GDB I=DH: EG:K>DJHAN HIJ9>:9 >C DJG LDG@ 45 H
H=DLC >C +:; 45 ) G:HEDCH>7A: ;DG I=: )+ H><C6A =6K: I=: 6C>HDIGDE>8
<I:CHDG L>I= I=: 6M>6A HNBB:IGN <O 6C9 <M <N "C
I=>H HIJ9N I=: 67DK: B:CI>DC:9 H6BEA:H L:G: HJ7?:8I:9 ID I=: ADLI:B
E:G6IJG: 6CC:6A>C< >C K68JJB L>I=>C I=: I:BE:G6IJG: G6C<: D;
R– R HIGDC< :;;:8I D; ADL I:BE:G6IJG: 6CC:6A>C< DC I=: )+
H><C6A D; EG:K>DJHAN ;DGB:9 7N γ>GG69>6I>DC E6G6B6<C:I>8 9:;:8IH =6H
7::C I=: XGHI I>B: G:K:6A:9
-=: 9:E:C9:C8: D; I=: 8DC8:CIG6I>DC D; ) DC I=: 9JG6I>DC D; K68
JJB 6CC:6A>C< D; H6BEA: 6I - R >H H=DLC >C ><
H ;DAADLH ;GDB >< 'H9:8G:6H:H 9JG>C< I=: 6CC:6A>C< 7N 67DJI
I>B:H -=: IG6CH;DGB6I>DC D; HE:8IG6 9JG>C< 6CC:6A>C< D; H6BEA:H
6I I:BE:G6IJG:H D; 6C9 RV 6H L:AA 6H I=:>G G:8DK:GN 9JG
>C< HJ7H:FJ:CI =DA9>C< >C I=: 6>G >H CDI IG>K>6A -=:G: EGD8::9H CDI DCAN
Fig. 2. )+ HE:8IG6 D; I=: γ>GG69>6I:9 <A6HH H6BEA:H 6C9 8DCI6>C>C< I=: :G7>JB
L>I= 6C9 6I G:HE:8I>K:AN 7:;DG: I=: 6CC:6A>C< -=: >GG69>6I>DC 9DH: L6H
:FJ6A ID N
Fig. 3. DC8:CIG6I>DC D; E6G6B6<C:I>8 9:;:8IH 'H >C H6BEA: 6H ;JC8I>DC D; K68JJB 6C
C:6A>C< I>B: 6I - R ,NB7DAH –:ME:G>B:CI HDA>9 A>C: –I=:DGN
6 9:8G:6H: >C I=: 8DC8:CIG6I>DC D; I=: ) G:HEDCH>7A: ;DG H><C6AH EG:
H:CI:9 >C >< 7JI I=: HE:8IGJB 8=6C<:H 6H >I >H 9:BDCHIG6I:9 >C ><
6 6C9 7
0: 7:A>:K: I=6I I=: K686C8N BDI>DC 6C9 <A6HH B6IG>M G:A6M6I>DC 9JG
>C< I=: ADL I:BE:G6IJG: 6CC:6A>C< 86JH: I=: G:DG>:CI6I>DC D; ) 6C9 G:
9J8I>DC D; I=:>G HNBB:IGN HD I=6I I=G:: B6>C 8DBEDC:CIH D; I=: <I:C
HDG 6G: H=>;I:9 ID <O TU− <N TU− 6C9
<M TU− >C I=: G;G:: H6BEA: ;I:G I=: ADC<I:GB
=DA9>C< D; I=: 6CC:6A:9 H6BEA: >C I=: 6>G I=: 8=6G68I:G>HI>8 E6G6B:I:GH
D; I=: )+ H><C6A <G69J6AAN G:IJGC ID I=: K6AJ:H D7H:GK:9 7:;DG: I=: 6C
C:6A>C< -=: )+ H><C6A D; ) >C H6BEA: L>I= 6I G G:B6>CH >C
I=: H6B: G:HDC6C8: B6<C:I>8 X:A9 8DGG:HEDC9>C< ID I=: 6K:G6<:9 HE:8
IGJB L>I= <PP 6C9 <⊥ 7JI >I >H HEA>I 9J: ID I=: 9:
8G:6H: D; I=: A>C: L>9I=
>< 6 H=DLH I=: 9:86N D; I=: B6>C H><C6A >CI:CH>IN >C I=: G;G::
H6BEA: 6C9 I=: G:HJAIH ;DG G 8DCI6>C>C< H6BEA:H 6C9 6G: <>K:C
>C >< 7 'DI: I=6I 6I I6CC B>C I=: >CI:CH>IN D; I=: )+ A>C: 6H
L:AA 6H >IH <;68IDG >C >< 6 >C8G:6H: 67CDGB6AAN -=>H ;68I =6H HD ;6G
CD :MEA6C6I>DC
UNCORRECTED PROOF
A.A. Konchits et al. Physica B: Physics of Condensed Matter xxx (xxxx) xxx-xxx
Fig. 4. 6 -=: )+ HE:8IGJB ;DG H6BEA: G ;G:: 6;I:G B>C 6CC:6A>C< 6I R -=:
HE:8IGJB 7:;DG: 6CC:6A>C< >H H=DLC >C >< 8JGK: b -=: )+ HE:8IGJB ;DG H6BEA:
6I G 6;I:G B>C 6CC:6A>C< 6I R 6C9 HJ7H:FJ:CI :MEDHJG: ID 6>G ;DG =
-=: HE:8IGJB 7:;DG: 6CC:6A>C< >H H=DLC >C >< 8JGK:
AA I=: G:HJAIH >C >< 6 6C9 7 6G: 9:H8G>7:9 7N ILD :MEDC:CI>6A
;JC8I>DCH I6CC caU:ME Iτ 7U:ME Iτ L>I= 8DCHI6CIH a,
b, τ1,τ29>;;:G:CI ;DG 9>;;:G:CI H6BEA:H 6H >I >H H::C ;GDB -67A:
-=: 8DBBDC EGDE:GIN D; 6AA H6BEA:H >H I=: EG:H:C8: D; ;6HI :MEDC:C
I>6A ;JC8I>DC L>I= τ B>C L=>8= >C9>86I:H ID I=: BDI>DC D; K686C
8>:H &DG:DK:G DC: 86C HJEEDH: I=6I I=: ) 8DCI6>CH I=: K686C8N D; HJA
;JG +:6AAN I=: HJA;JG =6H 6 B6M>BJB 9>;;JH>DC G6I: 6C9 I=: B>C>BJB
68I>K6I>DC :C:G<N ;DG 9>;;JH>DC 45 -=: 6CC:6A>C< 68I>K6I:H I=: BDI>DC
D; 6 HJA;JG 6IDB ID >IH K686C8N /H L=>8= >H >C I=: H:8DC9 H=:AA D; I=:
C:6G:HI :CK>GDCB:CI H 6 G:HJAI I=: ) 9>H6EE:6GH 7:86JH: 6 >C 67
H:C8: D; /,9D:H CDI G:K:6A E6G6B6<C:I>HB
-=: H:8DC9 :MEDC:CI>6A ;JC8I>DC 9:E:C9H DC I=: 6BDJCI D; G >C
H6BEA:H C6B:AN τ>H ADC<:G >C H6BEA:H L>I= A6G<:G G 6BDJCI :H>9:
I=>H G >C8G:6H:H I=: 8DCIG>7JI>DC D; I=: H:8DC9 :MEDC:CI -=>H ;68I H6NH
67DJI I=: HADL>C< 9DLC D; I=: A6II>8: G:A6M6I>DC >C EG:H:C8: D; G
"; 6;I:G I=: ADL I:BE:G6IJG: 6CC:6A>C< H6BEA: G:B6>CH DE:C >C I=:
6>G ;DG 6 ADC< I>B: 67DJI 96NH I=: )+ H><C6A >H 6ABDHI 8DBEA:I:AN
G:HIDG:9 7JI >I EGD8::9H HADLAN >< H=DLH I=: G:8DK:GN D; I=: )+
H><C6A >C H6BEA: 6I G
(C: 86C H:: >C >< I=6I 6C >C8G:6H: D; 6CC:6A>C< I:BE:G6IJG:
G:HJAIH >C 6 A>IIA: A6G<:G 9:86N D; H><C6A 7JI I=: G:8DK:GN EGD8:HH
Fig. 5. 6 =6C<: D; I=: ) 8DC8:CIG6I>DC 'HK:GHJH I=: 6CC:6A>C< I>B: >C H6BEA: G
;G:: ^6CC RV HFJ6G:H 6G: I=: :ME:G>B:CI6A ED>CIH 6C9 HDA>9 8JGK: >H I=: 86A8JA6I:9
I>B: ;JC8I>DC "CH:GI 9:BDCHIG6I:H 67CDGB6A 7:=6K>DG D; I=: )+ H><C6A 6I I6CC B>C
b. =6C<: D; I=: ) 8DC8:CIG6I>DC K:GHJH I=: 6CC:6A>C< I>B: -6CC ;DG 8>G
8A:H 6C9 ^6CC RV ;DG HFJ6G:H %>C:H 6G: 86A8JA6I:9 I>B: ;JC8I>DCH IG>6C<A:H 6G:
I=: :ME:G>B:CI6A ED>CIH ;DG C:L H><C6A "′HEA>I DZ ;GDB I=: B6>C H><C6A
Table 1
DCHI6CIH D; I=: ;JC8I>DC 9:86N
,6BEA: 'G6I c a b τ1B>C τ2B>C
<D:H BJ8= ;6HI:G ;I:G 6CC:6A>C< 6I -6CC R I=: ) 8DC8:CIG6
I>DC >C8G:6H:H ;DAADL>C< I=: ;JC8I>DC D; ⋅:ME I L=:G:6H 6;I:G
6CC:6A>C< 6I -6CC R I=: ) 8DC8:CIG6I>DC >C8G:6H:H 6H ;JC8I>DC
D; ⋅:ME I
"I >H LDGI= CDI>C< I=6I 7DI= I=: +6B6C 6C9 I=: )+ HE:8IGDH8DE>:H
8:GI6>CAN >C9>86I: I=6I G HJEEDGIH I=: HI67>A>IN D; I=: <A6HH B6IG>M %:I
JH B6@: HDB: HI6I:B:CIH 8DC8:GC>C< I=: C6IJG: D; I=: HIJ9>:9 E6G6
B6<C:I>8 8:CIG:H -=: 6M>6A HNBB:IGN D; <I:CHDG :K>9:C8:H I=6I ) >H 6
8DBEA:M -=: ;6HI :MEDC:CI>6A ;JC8I>DC D; I=: 8DC8:CIG6I>DC 9:86N ?JH
I>X:H I=6I I=: K686C8N >H DC: D; I=: 8DBEDC:CIH -=: 67H:C8: D; =NE:G
UNCORRECTED PROOF
A.A. Konchits et al. Physica B: Physics of Condensed Matter xxx (xxxx) xxx-xxx
Fig. 6. +:8DK:GN D; I=: )+ H><C6A >C I=: H6BEA: 9JG>C< >IH =DA9>C< >C I=: 6>G 6 6;I:G
6CC:6A>C< B>C 6I R 7 6;I:G G:6CC:6A>C< ;DG B>C 6I R
XC: HIGJ8IJG: >C I=: )+ HE:8IGJB >C9>86I:H ID I=: 67H:C8: D; I=: DLC
CJ8A:> HE>C >C I=: ) (CAN DC: 6IDB >C <A6HHN 6AADNH =6H CDC8DBE:C
H6I:9 :A:8IGDC HE>C L=>8= >H 6 L>I= 8DCX<JG6I>DC D; 4G59HE
-=: 6 6IDB =6H I=: CJ8A:> HE>C " :;DG: I=: >GG69>6I>DC D; H6B
EA:H 6 9D:H CDI G:K:6A 6 E6G6B6<C:I>8 H><C6A !DL:K:G I=: K686C8N
8DC8:CIG6I>DC >H <GDL>C< JE 6;I:G I=: >GG69>6I>DC "; I=: 6 E:A:8IGDC
=6K>C< 6 CDC8DBE:CH6I:9 HE>C 7DJC9H I=: 6 6IDB L>I= I=: HJA;JG K6
86C8N /, I=: :A:8IGDC HE>C 9:CH>IN DC I=: 6 CJ8A:> L>AA 7: 67DJI O:GD
6C9 8DCH:FJ:CIAN I=: =NE:GXC: HIGJ8IJG: >H 67H:CI -=: 9:;:8I 6/,>H
I=: BDHI EDHH>7A: 86C9>96I: ID 7: I=: ) HIJ9>:9 >C DJG H6BEA:H >C6AAN
I=: HI6I:B:CI 6I I=: :C9 D; E6G6<G6E= 67DJI I=: 76C9 D; 8B−>C
I=: +6B6C HE:8IGJB 7:ADC<H ID 6 8DBEA:M D; , : 6 8DGG:A6I:H L>I=
I=>H >9:6 67DJI I=: C6IJG: D; )
3. Summary
H ;DAADLH ;GDB I=: +6B6C HE:8IG6 I=: γ>GG69>6I>DC >C8G:6H:H I=:
6BDJCI D; :I=NA:C:A>@: , : :,HIGJ8IJG6A <GDJEH 9J: ID I=: <GDL>C<
G6I>D D; I=: CJB7:G D; : ID I=6I D; , 6IDBH -=: A6II:G >H 9J: ID I=: EG:
9DB>C6CI ;DGB6I>DC D; H>AK:GHJA;JG HIGJ8IJG6A JC>IH D; <, 6C9 < :,
>C I=: JCHIGJ8IJG:9 <G>9 D; I=: <A6HH
DG I=: XGHI I>B: >I >H 9:I:8I:9 I=6I I=: ADL I:BE:G6IJG: – R
6CC:6A>C< D; γ>GG69>6I:9 H6BEA:H 86JH:H 6 H><C>;>86CI JE ID ;DA9 9:
8G:6H: >C I=: CJB7:G D; E6G6B6<C:I>8 8:CIG:H 6C9 >C I=: ADL:G HNB
B:IGN D; I=: ) :CK>GDCB:CI HD I=6I <I:CHDG =6K>C< 7:;DG: I=: 6M
>6A HNBB:IGN <O <M <N 7:8DB:H BDCD8A>C>8 L>I=
<O <N 6C9 <M
-=: 9:86N D; I=: ) 8DC8:CIG6I>DC L>I= I=: 6CC:6A>C< I>B: >H 9:
H8G>7:9 7N I=: HJB D; ILD :MEDC:CI>6A ;JC8I>DCH I=: ;6HI 9:86N L>I=
τ B>C >H G:A6I:9 L>I= BDI>DC D; K686C8N 6C9 I=: ADC<I>B: DC:
L>I= τ B>C 9:E:C9>C< DC I=: G 8DC8:CIG6I>DC 8DGG:
HEDC9H ID I=: A6II>8: G:A6M6I>DC -=: 9:E:C9:C8: D; I=: ADC< G:A6M6I>DC
I>B: DC I=: G 8DC8:CIG6I>DC >C9>86I:H ID G HI67>A>O6I>DC D; I=: A6II>8:
HIGJ8IJG:
-=: G:8DK:GN D; E6G6B6<C:I>8 8:CIG:H >C I=: 6B7>:CI 6IBDHE=:G: 6;
I:G 6CC:6A>C< >C8G:6H:H I=: ) 8DC8:CIG6I>DC JE ID K6AJ:H L=>8= L:G:
G:8DG9:9 7:;DG: 6CC:6A>C< -=>H G:K:GH>7>A>IN >H I=: >BEDGI6CI @:N ;DG JC
9:GHI6C9>C< I=: ) C6IJG: -=: 9:;:8I 6/,>H I=: BDHI EGD767A: BD9:A
;DG I=: E6G6B6<C:I>8 8:CI:G HIJ9>:9 =:G:
>C6AAN I=: 76C9 D; 8B−>C I=: +6B6C HE:8IGJB 7:ADC<>C< ID
I=: 8DBEA:M , : 6 6 :,8DGG:A6I:H L>I= I=: EGDEDH:9 C6IJG: D;
I=: )
-=:G:;DG: I=: G:HJAIH D; I=>H HIJ9N H=:9 I=: A><=I DC I=: C6IJG: 6C9
7:=6K>DG D; 9:;:8IH >C I=: γ>GG69>6I:9 8=6A8D<:C>9: <A6HH:H :ME6C9>C<
EDHH>7>A>IN ID 8DCIGDA I=:>G EGDE:GI>:H
H I=: = <A6HH:H 6G: 8DCH>9:G:9 ID 7: HJ>I67A: B6I:G>6AH ;DG 6EEA>
86I>DC >C I:A:8DBBJC>86I>DC 9:K>8:H E6GI>8JA6GAN >C I=: HE68: L>I= 6C
>C8G:6H:9 G69>6I>DC 768@<GDJC9 I=: @CDLA:9<: D; C6IJG: 6C9 7:=6K>DG
D; I=: 9:;:8I HNHI:B >C I=: <A6HH:H B6@:H >I EDHH>7A: ID EG:9>8I 6 8=6C<:
>C I=:>G AJB>C:H8:CI EGDE:GI>:H JC9:G G69>6I>DC 8DC9>I>DCH
-=: D7I6>C:9 G:HJAIH =6K: H=DLC I=6I I=: HNHI:B D; E6G6B6<C:I>8
9:;:8IH >H 6 EGD7: ;DG HIGJ8IJG6A IG6CH;DGB6I>DCH D88JGG>C< >C I=: <A6HH
A:69>C< ID 6 8=6C<: >C I=: AD86A HNBB:IGN D; I=: :CK>GDCB:CI D; 9:;:8IH
;GDB I=: 6M>6A ID I=: BDCD8A>C>8 DC: -=: :HI67A>H=:9 :MIG:B:AN =><=
BD7>A>IN D; K686C8>:H 6C9 I=: EDHH>7>A>IN D; “FJ:C8=>C<”E6G6B6<C:I>8
9:;:8IH 9J: ID 6 HA><=I =:6I>C< D; <A6HH:H 8DCXGB 6 EDHH>7>A>IN ID 8DC
IGDA I=: EGD8:HH D; G69>6I>DC>C9J8:9 9:;:8I ;DGB6I>DC 6C9 ID EGDADC< I=:
LDG@ I:GB D; I=: 9:K>8:H 76H:9 DC < 6 :, <A6HH:H
CRediT authorship contribution statement
A.A. Konchits: DGB6A 6C6ANH>H V.O. Yukhymchuk: DGB6A 6C6AN
H>H S.V. Krasnovyd: 0G>I>C< G:K>:L :9>I>C<
Uncited Reference
45
Acknowledgments
-=>H LDG@ L6H E6GI>6AAN HJEEDGI:9 7N I=: )GD?:8I D; ', D; .@G6>C:
№[
References
45 #% 96B 1 3=6C< 9H =6A8D<:C>9: A6HH:H )G:E6G6I>DC )GDE:GI>:H 6C9
EEA>86I>DCH 0DD9=:69 )J7A>H=>C< %>B>I:9 E
45 // !6AN6C // ,IG:A8=J@ /( 2J@=NB8=J@ ! $:KH=NC 2 6KN9NJ@
&/ ,=:K8=J@ ,/ /DGDCNJ@ +DA: D; HIGJ8IJG6A DG9:G>C< DC DEI>86A EGDE:GI>:H D;
I=: <A6HH:H < 6 :,–G, )=NH>86 –
45 3=>A>CH@6N6 /' %6OJ@>C '$ /6A::K $ (7A6HDK :M,M <A6HH:H :;:8IH
9:CH>IN 6C9 HIGJ8IJG: # 'DCGNHI ,DA>9H –
45 % W:GK>C@6 !GJ7N >C # ,IJ@: G:CC>C< )GD8 I= "CI DC; (C BDGE=DJH
6C9 %>FJ>9 ,:B>8DC9J8IDGH -6NADGG6C8>H %DC9DC
45 // !6AN6C $DC8=>IH ,=6C>C6 ,/ $G6HCDKN9 (( %:7:9 !
$:KH=NC &/ ,=:K8=J@ / D9C6GJ@ /( 2J@=NB8=J@ )+ D; γ>C9J8:9 9:
;:8IH 6C9 I=:>G :;;:8IH DC I=: E=DIDAJB>C:H8:C8: >C I=: <A6HH:H D; I=:
< 6 :,–G,HNHI:B +69>6I )=NH =:B –
45 (" ,=EDINJ@ # >A>E:8@> $DO9G6H -, $6K:IH@NN +69>6I>DC>C9J8:9 9:;:8I
;DGB6I>DC >C 8=6A8D<:C>9: <A6HH:H # 'DCGNHI ,DA>9H – –
45 ( ,=EDINJ@ $DK6AH@>N - $6K:IH@NN + DADK8=6@ & )DE:H8J =:B>86A >C
I:G68I>DC D; 8=6A8D<:C>9: K>IG:DJH H:B>8DC9J8IDGH L>I= 67HDG7:9 >BEJG>I>:H >C
9J8:9 7N γ>GG69>6I>DC # (EID:A:8IGDC 9K &6I:G –
45 // !6AN6C /( 2J@=NB8=J@ 2 JA: $ (O<6 $# #:9GN@6 " "K6H=8=:C@D
& ,@DGN@ ! $:KH=NC " (A:@H:NJ@ )/ ->H=8=:C@D &/ ,=:K8=J@ &
)>6H:8@> )=DIDAJB>C:H8:C8: ;:6IJG:H 6C9 CDCA>C:6GDEI>86A EGDE:GI>:H D; I=:
< 6 :,–G,<A6HH:H (EI &6I:G –
45 "/ $>IN@ // !6AN6C ! $:KH=NC " "K6H=8=:C@D " (A:@H:NJ@ ((
%:7:9 %6@H=B>C6G6N6C6 & )>6H:8@> 6"CG, H>C<A: 8GNHI6A
CDK:A B6I:G>6A ;DG 9:I:8I>DC D; γG69>6I>DC 7N E=DID>C9J8:9 CDCA>C:6G DEI>86A
B:I=D9 # &6I:G ,8> &6I:G A:8IGDC –
45 \ $>IN@ /( 2J@=NB8=J@ :9DG8=J@ // !6AN6C " "K6H=8=:C@D "
(A:@H:NJ@ & ,@DGN@ %6@H=B>C6G6N6C6 & A'6<<6G A76HH6B
(( %:7:9 & )>6H:8@> %6H:G HI>BJA6I:9 E>:ODDEI>8H D; γ>GG69>6I:9
6"C, 6C9 6"CG, H>C<A: 8GNHI6AH # AADNH DBE9
–
45 "/ $>IN@ $ (O<6 / !6AN6C " "K6H=8=:C@D & )>6H:8@> 6"C,
C6CD8GNHI6AA>I:H 6H CDK:A B6I:G>6AH ;DG CDCA>C:6G DEI>86A 9:I:8I>DC D; <6BB6 G69>6
I>DC &+, 9K –
45 1>6 , 6886GD 3=6D & 6A8DC>:G> =:C 6BB6 G6N >GG69>6I>DC >C
9J8:9 DEI>86A 76C9 <6E K6G>6I>DCH >C 8=6A8D<:C>9: <A6HH:H 'J8A "CHIGJB &:I=D9H
)=NH +:H –
45 - ,8=L:>O:G ' ,6BHDC + &DDG: 0 !:L6@ ' )6NC: +6G::6GI=
9DE:9 8=6A8D<:C>9: <A6HH X7:G A6H:G A:8IDC %:II –
45 // !6AN6C "/ $>IN@ ! $:KH=NC " "K6H=8=:C@D %6@H=B>C6G6N6C6
&/ ,=:K8=J@ :9DG8=J@ & )>6H:8@> ;;:8I D; I:BE:G6IJG: DC I=: HIGJ8IJG:
6C9 AJB>C:H8:C8: EGDE:GI>:H D; < 6 :,G,<A6HH:H # %JB>C
–
45 // !6AN6C (2 $=NO=JC " "K6H=8=:C@D ! $:KH=NC " (A:@H:NJ@ )
-NH=8=:C@D () /DK@ 2/ JA>@ A:8IGDC>8 HIGJ8IJG: 6C9 DEI>86A EGDE:GI>:H D;
6%6, 6C9 6%6G, H>C<A: 8GNHI6AH CDK:A A><=I8DCK:GI
>C< B6I:G>6AH )=NH>86 –
45 $ &6>G6? (EI>86A 06K:<J>9: 6C9 %6H:GH >C "BEGDK:9 6AA>JB %6CI=6CJB ,JA
E=>9: A6HH )= I=:H>H .C>K:GH>IN D; ,DJI=6BEIDC ,DJI=6BEIDC .$
UNCORRECTED PROOF
A.A. Konchits et al. Physica B: Physics of Condensed Matter xxx (xxxx) xxx-xxx
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<A6HH + =>B>: –
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I>DCH >C K68JJB :K6EDG6I:9 6BDGE=DJH :,: XAB HIJ9>:9 7N +6B6C H86II:G
>C< # 'DCGNHI ,DA>9H –
45 2 ,6@6<J8=> - !6C6H=>B6 $ (=6G6 ,>BDC & &>I@DK6 ,IGJ8IJG6A
IG6CH;DGB6I>DC >C :x,−x ≤x≤ C:ILDG@ <A6HH:H HIGJ8IJG6A K6G>:I>:H >C
H=DGIG6C<: B:9>JBG6C<: 6C9 C6CDH8DE>8 H86A: )=NH +:K &6I:G
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–
45 / &>IH6 + !DADB7 %DK6H & /:G:H & "K6C96 - $DK68= ,E:8IGDH8DE>8 K>
9:C8: D; D:M>HI:C8: D; AJHI:GH 6H:9 DC %DL α 6C9 !><= -:BE:G6IJG: β :,
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GD6I>6
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45 !J6C< 0 !:L6@ #/ 699>C< :EDH>I>DC 6C9 8=6G68I:G>O6I>DC D; <:GB6
C>JB HJAE=>9: <A6HH EA6C6G L6K:<J>9:H (EI>8 MEG:HH –
45 1 06C< , J # 2J 1 3=6D ! -6D ,IGJ8IJG6A >CK:HI><6I>DCH D;
:,– 6,–9, 8=6A8D<:C>9: <A6HH:H JH>C< +6B6C HE:8IGDH8DEN ,DA>9 ,I6I:
DBBJC
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!DL H>AK:G >CYJ:C8:H I=: HIGJ8IJG: 6C9 E=NH>86A EGDE:GI>:H D; 8=6A8D<:C>9: <A6HH
:,,7, # 'DCGNHI ,DA>9H –
45 & 6A6@G>H=C6C &' $DO>8@> )DL:A:>I , =6<6I -% A;DG9 & &>I@DK6
GNHI6AA>O6I>DC :;;:8IH >C 6CC:6A:9 I=>C :,XABH E=DID9>;;JH:9 L>I= < #
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