Ne 17M / 02/ 08
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- ひさとも うみのなか
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1 Ne 17M / 02/ 08
2 Z N=20 sd pf 2 pf 2ħω 26 Ne 30 Ne 2 +, 4 + R 4/2 32 Ne 32 Ne δ 33 Na 1 32 Ne 32 Ne RI 240 MeV 32 Ne SAMURAI CsI(Na) CATANA 33 Na 1 32 Ne (3) kev, 2077(13) kev R 4/ Ne Ne δ 1.77(7) fm 32 Ne 30 Ne R 4/2 = 2.82, δ = ± 0.07 fm
3 Abstract In the island of inversion area (N 20, Z 10-12), it is known that the neutron magic number N=20 disappears and nuclei strongly deform. Theoretically, it is suggested that the energy gap between the sd shell and the pf shell is reduced in this region, and the 2ħω configuration in which the two neutrons occupy pf shell, dominates the ground state. Though the change in the shell structure plays an important role in the appearance of the island of inversion, it is not fully understood yet how the shell structure changes as the neutron number increases. Recent studies have revealed that island of inversion is expanded forwards the neutron-rich side, resulting that the deformation region spreads wider than the island of inversion. It is important to systematically investigate the change in the deformation of nuclei with the increase in the neutron number. In neon isotopes, the excitation energies of 2 + and 4 + states decreases and the energy ratio between the 2 + and 4 + states (R 4/2 ) increases from 26 Ne to 30 Ne showing the development of the nuclear deformation. Currently there are few available experimental data for 32 Ne, which is the most neutron-rich neon isotope in island of inversion, because of the experimental difficulty. In this study, we performed an in-beam γ-ray spectroscopy of 32 Ne by one proton removal reaction of 33 Na and inelastic scattering of 32 Ne on a carbon target to study excited states and derive quadrupole deformation length δ of 32 Ne. The experiments were carried out at RI Beam Factory at RIKEN, which provides high intense 32 Ne and 33 Na beams. The secondary beams of 32 Ne and 33 Na with 240 MeV/nucleon were produced by a projectile fragmentation reaction of 48 Ca on a beryllium target. Outgoing particles were detected using the SAMURAI spectrometer to identify the reaction channels. De-excitation γ rays were measured using the CsI(Na) scintillator array, CATANA. The excitation energies of the and 4+ 1 states of 32 Ne were measured to be 676(3) kev and 2077(3) kev, respectively, in the one proton removal reaction of 33 Na. The energy ratio R 4/2 =3.07 is close to R 4/2 =3.33(for rigid rotor), suggesting strong quadrupole deformation. The angular distribution of the transition in the inelastic scattering of 32 Ne was obtained and compared with the DWBA(Distorted-wave Born Approximation) calculation. The deformation length δ = 1.77(7) fm was obtained for 32 Ne, indicating the larger deformation than 30 Ne (R 4/2 = 2.82, δ = ± 0.07 fm). iii
4 BigRIPS SAMURAI SBT ICB BDC1, CATANA FDC SAMURAI FDC HODF NeuLAND, NEBULA Z A/Z Z A/Z i
5 BDC Ne Ne Ecis A 46 Appendix 46 A.1 CATANA CsI(Na) A.2 SAMURAI ii
6 A A A A A A iii
7 N= , 4+ 1 R 4/ ħω, 2ħω δ θ Na BigRIPS SAMURAI ICB BDC CATANA type1( ) type2( ) type3( ) CATANA FDC SAMURAI FDC HODF T OF F 3 F 7 (ns) T OF F 7 F 13 (ns) T OF F 3 F 7 (ns) T OF F 7 F 13 (ns) F13Q ICB E F13Q ICB E ( 31 Ne, C ) ( 31 Ne, C ) ( 32 Ne, C ) Z ( 31 Ne, C ) A/Z ( 31 Ne, C ) HODF24 Q ( 31 Ne, C ) 33 Na iv
8 4.12 ( 32 Ne, C ) 32 Ne Z ( 31 Ne, C 33 Na ) A/Z ( 31 Ne, C 33 Na ) X bdc2 X (calc) bdc2 (mm) Y bdc2 Y (calc) bdc2 (mm) θ beam,x θ beam,y β tgt ( 31 Ne 30 Ne) ( 31 Ne 30 Ne) ( 31 Ne 30 Ne) Na 32 Ne kev 33 Na 32 Ne E dep E sim Ne1401 kev E sim HODF HODF24 x θx lab (rad) θy lab (rad) ( 6 < θ lab < 8 mrad ) Ne Ne Ne Ne Ne ,4+ 1 R4/ δ A A A v
9 1.1 30,32 Ne 0ħω, 2ħω, 4ħω BigRIPS (A/Z Z=10 ) (A/Z Z=10 ) (X tgt, Y tgt ) (θ beam,x, θ beam,y ) β tgt vi
10 1 [1] N = 8, 20 [2],[3] N=16 [4] 1.1 N = 20, island of inversion [5] 1.1 Z(7 13 N N=20 2ħω [6] 1.2 N=20 1f 7/2 1d 3/2 1d 3/2 N = 20 1f 7/2 1d 3/ f 7/2 2ħω 1
11 1.2 N=20 1f 7/2 1d 3/2 2ħω 1.1 (, big island of deformation)[7] N=26 38 Mg [8] 32 Ne ( ) 2009 [9] 2019 [10] (12) kev (15) kev , 4+ 1 R 4/2 N, 2 + 1, 4+ 1 R 4/2 R 4/2 2 E(I) = I(I + 1)ħ2 2I (1.0.1) R 4/2 3.3 I I R 4/2 34,36,38 Mg N=12,14,16 R 4/2 3 R 4/2 N= Ne R 4/2 = 2.99(6) [11] 2
![1.3 2 + 1, 4+ 1 R 4/2 [10] (MeV) (MeV) R 4/2 EKK(extended Kuo-Krenciglowa) [11] 0ħω, 2ħω 1.](/docs-images/101/148139623/images/12-1.jpg "4 0ħω, 2ħω [12] 2ħω N=19 23 70% N N=26 0ħω 2ħω 50% 1.4 Mg 0ħω, 2ħω [12] N( A) 0ħω, 2ħω 2ħω 0ħω SDPF-M SDPF-M+p 1/2 0ħω, 2ħω, 4ħω 1.")
12 , 4+ 1 R 4/2 [10] (MeV) (MeV) R 4/2 EKK(extended Kuo-Krenciglowa) [11] 0ħω, 2ħω 1.4 0ħω, 2ħω [12] 2ħω N= % N N=26 0ħω 2ħω 50% 1.4 Mg 0ħω, 2ħω [12] N( A) 0ħω, 2ħω 2ħω 0ħω SDPF-M SDPF-M+p 1/2 0ħω, 2ħω, 4ħω ,32 Ne 0ħω, 2ħω, 4ħω (%) 2 SDPF-M[13] EKK 3
![[11] 32 Ne 2ħω 30 Ne EKK 32 Ne 2 +, 4 + 2ħω, 4ħω EKK ( 1.3) 32 Ne 1.1 30,32 Ne 0ħω, 2ħω, 4ħω (%)[10] SDPF-M[13] EKK[11] 0ħω 2ħω 4ħω 0ħω 2ħω 4ħω 30 Ne 3.9 74.2 33.0 0.5 19.8 68.1 32 Ne 4.7 82.5 12.7 1.](/docs-images/101/148139623/images/13-0.jpg "8 36.2 51.9 δ 1.5 [14] δ β δ = Rβ (R = r 0 A 1/3 ) N = 18 22 δ N = 24 2 (AMPGCM[15], SDPF-M[13] N = 22( 32 Ne) 1.5 (a) (b) δ [14] N δ(fm) δ p.")
13 [11] 32 Ne 2ħω 30 Ne EKK 32 Ne 2 +, 4 + 2ħω, 4ħω EKK ( 1.3) 32 Ne ,32 Ne 0ħω, 2ħω, 4ħω (%)[10] SDPF-M[13] EKK[11] 0ħω 2ħω 4ħω 0ħω 2ħω 4ħω 30 Ne Ne δ 1.5 [14] δ β δ = Rβ (R = r 0 A 1/3 ) N = δ N = 24 2 (AMPGCM[15], SDPF-M[13] N = 22( 32 Ne) 1.5 (a) (b) δ [14] N δ(fm) δ p.p δ C AMPGCM[15]( ) SDPF-M[13]( ) 0ħω 32 Ne 33 Na 1 32 Ne 32 Ne 32 Ne RI 240 MeV 32 Ne SAMURAI 4
14 CsI(Na) CATANA 32 Ne
15 ( kev kev ) % E lab γ E lab γ = Eγ cm 1 γ(1 β cos θ) (2.1.1) E cm γ θ 2.1 γ, β v c γ = 1 1 β 2, β = v c (2.1.2) θ θ CATANA 100 θ 2.1 θ 60% v θ 6
16 Na 1 1d 3/ Ne (spectroscopic factor) Na (Distored-wave Born Approximation, DWBA DWBA 7
![3 2016 11 RI (RIBF) 2 BigRIPS 31 Ne, 32 Ne 3.1 RI BigRIPS SAMURAI 3.1.1 BigRIPS SRC 345 MeV 48 Ca F0 ( ) 15 mm Be 33 Na 32 Ne BigRIPS(Big RI Particle Separator)[16] 3.](/docs-images/101/148139623/images/17-0.jpg "1 BigRIPS 3.1 BigRIPS 345 MeV/u 48 Ca F0 Be 15 mm 32 Ne BigRIPS SAMURAI F7,F13 TOF F5 Bρ F13 ICB E F3,F5,F7 3 mm F13 0.5 mm 2 ( PMT ) F7 F13 TOF F5 8")
17 RI (RIBF) 2 BigRIPS 31 Ne, 32 Ne 3.1 RI BigRIPS SAMURAI BigRIPS SRC 345 MeV 48 Ca F0 ( ) 15 mm Be 33 Na 32 Ne BigRIPS(Big RI Particle Separator)[16] 3.1 BigRIPS 3.1 BigRIPS 345 MeV/u 48 Ca F0 Be 15 mm 32 Ne BigRIPS SAMURAI F7,F13 TOF F5 Bρ F13 ICB E F3,F5,F7 3 mm F mm 2 ( PMT ) F7 F13 TOF F5 8
18 X ( Bρ = Bρ X ) D (3.1.1) Bρ D = 3300 mm Bρ BigRIPS 31 Ne, 32 Ne 2 31 Ne 32 Ne F1 (Al) (mm) 8 10 F5 (Al) (mm) 5 5 F1 (mm) ±120 ±100 F2 (mm) ±5 ±8 F5 (mm) ±110 ±50 F7 (mm) ±5 ±20 D1 (Tm) D2 (Tm) SAMURAI BigRIPS SAMURAI Superconducting Analyzer for MUlti-particle from RAdio Isotope Beam [17] 3.2 SAMURAI, 2.15 g/cm 2 SAMURAI HODF24 (NeuLAND,NEBULA) SAMURAI FDC1,2 CATANA 9
19 3.2 SAMURAI SBT BDC SAMURAI HODF24 (NeuLAND,NEBULA) SAMURAI FDC1,2 CATANA SAMURAI SBT SBT(Scintillator for Beam Trigger) F13 F7-F13 TOF ICB ICB(Ion Chamber for Beam) F13 E 1 P10 (Ar90%,CH 4 10%) 3.3 ICB 3.3 ICB mm 10
20 BDC1,2 BDC(Beam Drift Chamber) BDC1 BDC BDC (X,X ) (Y,Y ) 8 (XX YY XX YY ) X(Y) X (Y ) 2.5 mm 16 5 mm 50 torr i-c 4 H BDC mm CATANA CATANA CAesium iodide array for γ-ray Transition in Atomic Nuclei at high isospin Asymmetry 3.5 CATANA,, CsI(Na) 1,2 ( ) 3,4 ( ) 5 CATANA CsI(Na) θ 10 ϕ 18 CATANA 3 ( 3.5 (type1) (type2) (type3)) 3.6,3.7, CATANA 11
21 3.5 CATANA,, CsI(Na) 3.2 θ( )
22 図 3.6 結晶 type1(青色) の図面 図 3.7 結晶 type2(水色) の図面 図 3.9 CATANA の写真 (ビームラインに設置前) 13 図 3.8 結晶 type3(緑色) の図面
23 85 mm 12 mm(2.15 g/cm 2 ) , mm FDC1 FDC1(Forward Drift Chamber 1) 3.12 FDC1 (0 ) X,X ±30 U,U V,V 3 14 (XX UU VV XX UU VV XX ) X(U,V) X (U,V ) 5 mm mm 50 torr i-c 4 H FDC1 mm 14
24 SAMURAI SAMURAI SAMURAI 2.9T 3.13 SAMURAI 3.13 SAMURAI mm FDC2 FDC2(Forward Drift Chamber 2) SAMURAI 3.14 FDC2 FDC (0 ) X,X ±30 U,U V,V 3 14 (XX UU VV XX UU VV XX ) X(U,V) X (U,V ) 10 mm mm 1 He+50%C 2 H 6 15
25 図 3.14 FDC2 の概略図 単位は mm HODF24 HODF24(HODoscope for Fragment 24) はプラスチックシンチレータ (長さ 1200 mm, 幅 100mm, 厚さ 10mm) 24 本 から構成される 図 3.15 に HODF24 の概略図を示す プラスチックシンチレータの上下には PMT が取り付けられてい る FDC2 の後方に設置され エネルギー損失 E と飛行時間 TOF を測定することにより Z の識別を行った 図 3.15 HODF24 の概略図 単位は mm NeuLAND, NEBULA NeuLAND と NEBULA は SAMURAI 磁石下流に設置された中性子検出器である NeuLAND はプラスチックシンチ レータ (50 mm 50 mm 2500 mm) が 400 本 (8 層) と VETO シンチレータ 8 本 NEBULA は 2 種類のプラスチックシ 16
26 (120 mm 120 mm 1800 mm, 10 mm 320 mm 1900 mm) 120 (4 ) 24 (2, VETO) Beam SBT1,2 PMT 3.3 Run No. 31 Ne 230 MeV/u C Beam Ne 240 MeV/u Empty Beam Ne 240 MeV/u C Beam Ne 250 MeV/u Empty Beam
27 4 Z ( ) Y X Z Y Z Z β ( E) Z (log ( 2mec2 I β 2 ) log (1 β 2 ) β 2 ) (4.1.1) I ICB m e β F7 F13 T OF F 7 F 13 F L F 7 F 13 (Flight Length) β = F L F 7 F 13 T OF F 7 F 13 c (4.1.2) T OF F 7 F 13 = t F 13 t F 7 F7,F13 t F 7, t F 13 PMT A/Z A/Z A Z = ebρ m u cβγ m µ e Bρ (4.1.3) F3 F7 T OF F 3 F 7 F7 F13 T OF F 7 F 13 SBT Q F 13 ICB E ICB T OF F 3 F 7 (ns) T OF F 7 F 13 (ns)
28 TOF T OF F 3 F 7 T OF F 3 F 7 ±3σ T OF F 3 F 7 T OF F 3 F T OF F 3 F 7(ns) T OF F 7 F 13(ns) 4.2 T OF F 3 F 7(ns) T OF F 7 F 13(ns) Q F 13 E ICB 4.3 TOF Q F 13 E ICB 3σ Q F 13 E ICB F13Q ICB E 4.4 F13Q ICB E Ne C A/Z 5.0% Ne C
29 4.5 ( 31 Ne, C ) 4.6 ( 31 Ne, C ) 4.7 ( 32 Ne, C ) Ne 32 Ne ( (%)) ( (%)) 34 Na (9.4%) 33 Na (21.0%) (21.1%) 32 Na (28.6%) (0.5%) 32 Ne (0.4%) (23.4%) 31 Ne (2.9%) (19.7%) 30 Ne (40.7%) (15.5%) 31 F (0.04%) 29 F (1.1%) (9.3%) 20
30 4.8, y (Z),x (A/Z) σ Z ( 31 Ne, C ) 4.9 A/Z ( 31 Ne, C ) 4.2 (A/Z Z=10 ) 31 Ne,C 32 Ne,C σ σ Z= Z= Z= A/Z= A/Z= A/Z= Z Z HODF24 Q 4.10 HOF24 ID12 (ns) Q Z=10 1 (Q = p 0 + p 1 t) Q Q cor Q corr = Q p 0 + p 1 t (4.1.4) Q cor Z Q cor Z Z = p 0 + p 1 Q coor + p 2 Q 2 corr (4.1.5) Q cor Z 21
31 4.10 HODF24 (ns) Q A/Z A/Z Bρ FDC1,2 Bρ Bρ = (i,j,k,l,m,n)=(3,2,3,2,3,3) (i,j,k,l,m,n)=0 C ijklmn X i fdc1y j fdc1 θk x,fdc1θ l y,fdc1x m fdc2θ n x,fdc2 (4.1.6) C Geant4 Bρ FDC1 FDC2 HODF24 F L ROOT TMultiDimFit X fdc1, Y fdc1, θ x,fdc1, θ y,fdc1, X fdc2, θ x,fdc2 Bρ 4.11,4.12 A/Z Z Ne C 33 Na Ne C 32 Ne 4.13, y (Z),x (A/Z) 4.3 σ 22
32 4.11 ( 31 Ne, C ) 33 Na 4.12 ( 32 Ne, C ) 32 Ne 4.13 Z ( 31 Ne, C 33 Na ) 4.14 A/Z ( 31 Ne, C 33 Na ) 4.3 (A/Z Z=10 ) 31 Ne,C 32 Ne,C σ σ Z= Z= Z= A/Z= A/Z= A/Z=
33 4.2 x,y BDC2 31 Ne BDC2 BDC1,BDC2,FDC1 BDC1,BDC2,FDC1 x,y,z X bdc1, Y bdc1, Z bdc1, X bdc2, Y bdc2, Z bdc2, X fdc1, Y fdc1, Z fdc1, BDC2 X bdc1 X fdc1 X (calc) bdc2 BDC2 X bdc2 X (calc) bdc mm mm X bdc2 Y bdc2 Y bdc2 Y (calc) bdc Y bdc mm 4.15 X bdc2 X (calc) bdc2 (mm) 4.16 Y bdc2 Y (calc) bdc2 (mm) X tgt, Y tgt 4.17 X tgt, Y tgt X bdc1 X bdc2 Y bdc1 Y bdc2 ( 40 mm ) Xtgt 2 + Ytgt 2 < 40 mm X tgt σ -1.1 mm, 6.2 mm Y tgt σ -0.9 mm, 5.2 mm 24
34 4.17 x(mm) y(mm) θ beam,x, θ beam,y ( ) Xbdc2 X bdc1 θ beam,x = arctan Z bdc2 Z bdc2 ( ) Ybdc2 Y bdc1 θ beam,y = arctan Z bdc2 Z bdc2 (4.2.7) (4.2.8) θ beam,x, θ beam,y (rad) 4.18, Ne θ beam,x σ 0.0 mrad, 3.2 mrad θ beam,y σ 0.4 mrad, 4.2 mrad 4.18 θ beam,x (rad) 4.19 θ beam,y (rad) 25
35 β tgt β tgt Ne 30 Ne σ 0.61, β tgt (X tgt, Y tgt) (θ beam,x, θ beam,y ) β tgt 31 Ne,C σ X tgt (mm) Y tgt (mm) θ beam,x (mrad) θ beam,y (mrad) β tgt ( 137 Cs, 22 Na, 60 Co, 88 Y) ID=10 (ch) (kev)
36 1 (kev) 4.5 (kev) 137 Cs Na 511, Co 1173, Y 898, (kev) θ β tgt θ Ne 30 Ne 800 kev P. Fallon [27] 30 Ne g.s. 27
37 4.22 ( 31 Ne 30 Ne) 4.23 ( 31 Ne 30 Ne) ( ) ( ) Ne 30 Ne ( ) 4.24 ( 4.23)
38 4.24 ( 31 Ne 30 Ne) ( 4.23) Ne 33 Na 32 Ne (3) kev 1401(13) kev 2 I. Murray [10] g.s. 709(12) kev (15) kev Na 32 Ne 28,30,32 Ne kev θ Z +10 mm 29
39 30 Ne Ne (2) kev 689(4) kev +15 kev Ne ( ) 1280(4) kev 1304(3) kev [26] 30 Ne ( ) 774(2) kev 792(4) kev [27], 800(7) kev [14] 32 Ne ( ) 676(3) kev 709(12) kev [10], 722(7) kev [9] 32 Ne ( ) 1401(13) kev 1410(15) kev [10] kev 676 kev ( ) 2077 kev 676 kev 33 Na 32 Ne 1401±3σ kev 4.26 σ 1401 kev ±3σ kev 700 kev 676 kev 1401 kev kev 33 Na 32 Ne Na 32 Ne 4 + σ( 33 Na 32 Ne(4 + )) σ( 33 Na 32 Ne(4 + )) = p0/ϵ frag N (us) 33 Na A t N 0 (4.3.9) N (us) 33 Na 33 Na ϵ frag p 0 30
40 32 Ne 4 + A = 12(g/mol) t = 2.15(g/cm 2 ) N 0 = (mol 1 ) N (us) 33 Na = Ne 4 + Geant4 Geant4 E dep 1000 kev 10 E dep (kev) kev E γ ( 4.5 ) σ i a i, b i a i σ i (E γ ) = 2 2 ln 2 Ebi γ (4.3.10) a i 2.35 Ebi γ (4.3.11) σ i (E γ ) ID=10 a i b i (ID=10) (kev) σ(kev) E dep E dep σ i (E dep ) E sim 4.28 E sim (kev)
41 kev E dep (kev) E dep kev E sim(kev) E sim E dep σ i( ) 32 Ne 100 γ E γ 1401keV z β z σ X 0.0 mm σ 5.3 mm Y 0.0 mm σ 7.6 mm Z mm E sim Ne 1401 kev E sim (kev) ( 100 ) 32
42 F sim (E γ ) p 0, p 1, p 2 p 0 F sim (E γ ) + exp (p 1 + p 2 E γ ) (4.3.12) Ne 4 + p 0 = (kev) (FDC1,2 HODF24) FDC1,2 FDC1,2 HODF24 Z=10 FDC1,2 Z= FDC1 FDC FDC1,FDC2 100%, 97.2% HODF24 HODF24 2 ( ) 4.32 Z 4.33 HODF24 x (mm) 32 Ne FDC2 x = 300, 400(mm) HODF24 4 mm 4 mm HODF24 HODF HODF24 32 Ne 98.0% ϵ frag 32 Ne ϵ frag = = % 33
43 4.32 HODF24 2 Z 4.33 HODF24 x (mm) HODF24 33 Na 32 Ne 4 + σ( 33 Na 32 Ne(4 + )) σ( 33 Na 32 Ne(4 + )) = p0/ϵ frag N (us) 33 Na A t N 0 (4.3.13) = / (g/mol) (g/cm 2 ) (mol 1 ) (4.3.14) = 1.29 (mb) (4.3.15) 34
44 beam BDC1 BDC2 (X bdc1, Y bdc1, X bdc2, Y bdc2,) frag FDC1 (X tgt, Y tgt, X fdc2, Y fdc2,) θ lab beam frag θ lab σ θ lab 31 Ne θ lab x θx lab, θy lab 4.34, 4.35 θ lab x x σ θ lab x σ θ lab = 2.2 mrad σ y θ lab = 3.1 mrad, θy lab (rad) = 2.2 mrad y 4.34 θx lab (rad) 4.35 θy lab (rad) Ne 32 Ne θ lab 2 mrad E γ 774 kev β 0.61, X 0.0 mm σ 5.3 mm Y 0.0 mm σ 7.6 mm Z mm < θ lab < 8mrad 35
45 4.36 ( 6 < θ lab < 8 mrad ) (kev) p 0 dσ dω = p 0 A 1 (4.4.16) N (us) t N 30 0 W bin 2π sin θ lab Ne N (us) 30 Ne 30 Ne A=12 g/mol t=2.15 g/cm 2 N 0 = mol 1 N (us) 30 Ne = W bin = 2 mrad Ne θ lab (deg) dσ dω (mb/sr) 36
46 Ne θ lab (deg) dσ dω (mb/sr) 32 Ne 32 Ne Ne A = 12 g/mol t = 2.15 g/cm 2 N 0 = mol 1 N (us) 32 Ne = W bin = 3 mrad Ne θ lab (deg) dσ dω (mb/sr) Ne Ecis97 Ecis97[18] δ Ecis97 ( ) δ 37
47 Ecis97 T. Furumoto Global Optical Potential[19],[20] G-Matrix (CEG07[21],[22]) Global Density[23] folding Ecis97 U(r, E) U(r, E) = V V (r, E) V D (r, E) iw V (r, E) iw D (r, E) (4.4.17) [24] r E V i, W i (i = V, D) V, D V V (r, E) = V V (E)f(r, R V, a V ) (4.4.18) V D (r, E) = 4a D V D (E) d dr f(r, R D, a D ) (4.4.19) W V (r, E) = W V (E)f(r, R V, a V ) (4.4.20) W D (r, E) = 4a D W D (E) d dr f(r, R D, a D ) (4.4.21) V i (E), W i (E) (i = V, D) f(r, V i, a i ) (i = V, D) Woods-Saxon 1 f(r, R i, a i ) = 1 + exp ( r ai R i ) (4.4.22) R i, a i (i = V, D) diffuseness ,4.40 (fm) (MeV) Global Optical Potential[19],[20] 240 MeV/u 32 Ne 4.39 (fm) (MeV) [20] 4.40 (fm) (MeV) [20] 38
48 230 MeV/u 30 Ne 240 MeV/u 32 Ne Ne (230MeV/u) 32 Ne (240MeV/u) V V (MeV) R V (fm) a V (fm) V D (MeV) R D (fm) a D (fm) W V (MeV) R V (fm) a V (fm) W D (MeV) R D (fm) a D (fm) Ecis97 tan θ Lab = 1 sin θ CM γ g cos θ CM + β g /β CM (4.4.23) ( ) Lab ( dω γ 2 g (β g /β CM + cos θ CM ) 2 + sin 2 θ CM) 3/2 = dω γ g (1 + cos θ CM β g /β CM ) (4.4.24) ( ) θ CM, θ Lab β g, γ g v g β g = vg c, γ 1 g = 1 β 2 g 4.42 ( ) 39
49 4.41 [ ] dσ dω (θ exp) = exp 2π 0 dϕ π 0 [ ] ) dσ sin θdθ dω (θ) 1 ( cal 2πσ 2 exp α2 2σ 2 (4.4.25) [ dσ dω (θ)] σ cal σ = 3.1 mrad α sin 2 α 2 = sin2 θ exp 2 + sin2 θ 2 2 sin θ exp 2 sin θ 2 ( sin θ exp 2 sin θ 2 + cos θ exp 2 cos θ ) 2 sin ϕ (4.4.26)
50 Ne 4.43 δ = 1.62(2) fm 30 Ne δ S. Michimasa [14] δ = ± 0.07 fm P. Doornenbal [25] δ = 1.98(11) fm 2 + ( ) σ(2 + 1 )=14.4(14) mb 12.7(3) mb Ne 32 Ne 4.44 δ = 1.77(7) fm Ne 41
51 5 32 Ne 2 (676,1401 kev) 32 Ne 5.1 kev 5.1 EKK [11] SDPF-M[13] 32 Ne 676 kev,2077 kev 2 2 +, kev 2077 kev 2 +, Ne kev EKK [11] SDPF-M[13] 676 kev 2077 kev 2 +, R 4/2 = ,4+ 1 R 4/2 EKK 32 Ne (N=22) 26 Ne (N=16) 30 Ne (N=20) 2 +, 4 + R 4/2 30 Ne (N=20) Z=20 32 Ne 30 Ne R 4/2 EKK 42
52 ,4+ 1 R4/ ( ) 4+ 1 ( ) (kev) R 4/2 EKK 32 Ne (N=22) δ Ne N= Ne 28 Ne 30 Ne δ R 4/2 N=20 32 Ne δ 2 N = δ δ 32 Ne 34 Ne 43
![5.3 δ δ(fm) SDPF-M[13],](/docs-images/101/148139623/images/53-1.jpg "AMPGCM[15] 32 Ne (N=22)")
53 5.3 δ δ(fm) SDPF-M[13], AMPGCM[15] 32 Ne (N=22) 44
54 6 32 Ne δ 33 Na 1 32 Ne 32 Ne RI 240 MeV 32 Ne SAMURAI CsI(Na) CATANA 33 Na 1 2 (676(3) kev, 1401(13) kev) , R 4/ Ne Ne δ 1.77(7) fm 32 Ne 30 Ne R 4/2 = 2.82, δ = ± 0.07 fm ( ) 45
55 A A.1 CATANA CsI(Na) 100 ( ) A.1 A.2 A.1 A.2 CsI(Na) CATANA 3 ( A.1 (type1) (type2) (type3) 3 3.6, 3.7, 3.8) 1 mm 85 mm 12 mm(2.15 g/cm 2 ) , mm 2 mm ( )7.92 cm ( )8.26 cm CATANA 140cm 46
56 A.2 SAMURAI T. Tomai Photogrammetry System A.3 A.3 SAMURAI mm 47
57 A.3 Distored-wave Born Approximation DWBA [28],[29],[30] A.3.1 X(a,b)Y dσ dω = M axm by (2πħ 2 ) 2 k b k a T 2 (8.3.1) M ax, M by (a+x) (b+y) k a, k b a,b T V T = exp ( i k b r ) Y V X exp (+i k a r ) d r (8.3.2) exp ( i k b r ), exp (+i k b r ) { ħ2 2 + U( } r ) ψ i ( r ) = E i ψ i ( r ) (8.3.3) 2M i ψ i ( k i, r ) T = ψby ( k b, r ) Y V X ψax( k a, r ) d r (8.3.4) A.3.2 X(a,a )X dσ dω = M ax 2 k a (2πħ 2 ) 2 T 2 (8.3.5) k a T = ψa X ( k a, r ) X V X ψax( k a, r ) d r (8.3.6) ( R 0 ) { R(θ, ϕ) = R } α lm Yl m (θ, ϕ) lm (8.3.7) Yl m (θ, ϕ) U(r, R(θ, ϕ)) U(r, R(θ, ϕ)) = U(r, R 0 ) + R 0 { lm α lm Y m l (θ, ϕ) } du dr 0 + (8.3.8) 48
58 2 V coup V coup = U(r, R(θ, ϕ)) U(r, R 0 ) (8.3.9) 1 ( ) V coup (1) du = R 0 α lm Yl m (θ, ϕ) dr 0 lm (8.3.10) α lm iħ z mħ ( ) b + lm, b lm α lm = β l ( blm + ( 1) m b + ) 2l + 1 lm (8.3.11) β l α lm 1 (ħω) βl 2 = 0 l α lm 2 0 m= l (8.3.12) X V (1) X = 1ħω, l l V (1) 0, 0 + (8.3.13) ( ) β l du = R 0 Yl m (θ, ϕ)ψ ax (8.3.14) 2l + 1 dr 0 dσ dω = M 2 ax (2πħ 2 ) 2 k a k a β 2 l 2l + 1 ( ) ψa du X R 0 Yl m (θ, ϕ)ψ ax d r dr 0 2 (8.3.15) β 2 l l β l β δ 49
59 A.4 (z, ρ, ϕ) X,a 2 ( X 32 Ne a 12 C ) c = ħ = 1 m i (i=x,a) β i, p Lab i, Ei Lab (i=x,a) β g β a = 0 β g = mγ Xβ X + mγ a β a m X γ X + m a γ a (8.4.1) = p Lab X EX Lab + m a (8.4.2) β g p CM X, ECM X ) ( ) γg γ g β g ( E CM X p CM X = ) ( E Lab X γ g β g γ g p Lab X (8.4.3) 1 γ g = 1 β 2 g A.4.1 z, ρ p Lab X,z, plab X,ρ θlab tan θ Lab = plab X,ρ p Lab X,z (8.4.4) E Lab X p Lab X,z p Lab X,ρ = γ g γ g β g 0 γ g β g γ g E CM X p CM X,z p CM X,ρ (8.4.5) θ CM tan θ Lab = 1 γ g sin θ CM cos θ CM + β g /β CM (8.4.6) A.4.2 dσ ( ) Lab dσ dω Lab = dω z ( ) ϕ CM = ϕ Lab dω = sin θdθdϕ ( ) CM dσ dω CM (8.4.7) dω dω CM dω Lab = sin θcm dθ CM sin θ Lab dθ Lab (8.4.8) = d(cos θcm ) d(cos θ Lab ) 50 (8.4.9)
60 8.4.6 cos θ CM 1 tan θ Lab cos 3 θ Lab d(cos θcm ) d(cos θ Lab ) = 1 (cos θ CM β g /β CM + 1) γ g sin θ CM (cos θ CM + β g /β CM ) (8.4.10) ( d(cos θ CM ) γ 2 d(cos θ Lab ) = g (β g /β CM + cos θ CM ) 2 + sin 2 θ CM) 3/2 γ g (1 + cos θ CM β g /β CM ) (8.4.11) ( ) Lab dσ = d(cos ( θcm ) dσ dω d(cos θ Lab ) dω ( γ 2 g (β g /β CM + cos θ CM ) 2 + sin 2 θ CM) 3/2 = ) CM (8.4.12) γ g (1 + cos θ CM β g /β CM ) ( ) CM dσ (8.4.13) dω 51
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