~（130）Cs手征双重带研究
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摘要
利用重离子融合蒸发反应124Sn(11B,5n)130Cs布居了130Cs的高自旋态,11B束流由中国原子能科学研究院的HI-13串列加速器提供,束流能量为65MeV,129Cs是其中一个布居较强的副反应道。利用多普勒线移衰减法对这两个原子核的能级寿命进行了测量。
130Cs核芯具有软的γ形变;核芯外的价质子位于高j低Ω轨道,具有粒子特性;而价中子位于高j高Ω轨道,具有空穴特性。两种不同特性的价核子具有相反的形状驱动效应,导致130Cs具有稳定的三轴形变。TRS计算结果也显示130Cs核具有较大的三轴形变满足产生手征双重带的条件。实验重建了130Cs的候选手征双重带,测量能级寿命,提取了电磁跃迁几率。对130Cs候选手征双重带的激发能、旋称劈裂、约化电磁跃迁几率比、绝对电磁跃迁几率进行了比较分析,实验结果表明130Cs的候选手征双重带具有能量近似简并的能级;旋称劈裂较小而且随自旋的变化平滑;约化跃迁几率比表现出明显的奇偶自旋振荡;具有相近的绝对电磁跃迁几率值,较小的B(E2)值和B(M1)值典型的奇偶自旋振荡。利用PRM理论模型计算了130Cs手征双重带的激发能和电磁跃迁几率,在较高自旋处理论计算很好的再现了实验结果。对核芯、价质子、价中子三个角动量间的有效角度以及总角动量在三个主轴投影分布几率进行了计算,计算结果表明在较高自旋处130Cs表现出静态手征特性。
论文对A-130区的候选手征双重带进行了分析。122-132Cs的系统分析认为在126-130Cs奇奇核的候选手征双重带具有好的手征特性。还对已经提取能级寿命的候选手征双重带的电磁跃迁几率进行了分析,分析显示该核区的手征双重带具有较小的B(E2)值和典型的B(M1)值奇偶自旋振荡。对于该核区的能级近简并的伙伴带不一定是手征双重带。
测量了129Cs的三条主要转动带的能级寿命,提取了电四极矩值。实验结果指出,πh11/2组态的转动带的电四极矩值小于πg7/2和πd5/2转动带,这可能主要是由于不同质子轨道的三轴形变驱动效应不同导致;在较高自旋处三个带的Qt值出现明显的变化,这主要来至于h11/2质子或中子的顺排。
Chiral symmetry exists commonly in nature. Since the chiral symmetry broken in triaxial-deformed nuclei has been predicted by Frauendorf and Meng in 1997, nuclear chiral structure has attracted significant interest of both theoretical and experimental studies. More than 20 candidate chiral bands with the same parity and degenerate energy have been reported in odd-odd, odd-A, and even-even nuclei of the A~100,130,190 mass regions in experiments. The cores in these nuclei are soft toγ-deformation;, the proton (or neutron) Fermi surface lies in the high-j low-Ωorbital (particle-like), and the neutron (or proton) Fermi surface is located in the middle or upper of high-j subshell (hole-like). These nuclei are suggested to have stable triaxial deformation due to the different deformation-driving effects of the hole-like and particle-like valence nucleons. In the triaixal-deformed nuclei, the core’s collective angular momentum will favour alignment with the intermediate“i-axis”, which has the largest moment of inertia. The particle-like nucleon tends to align their angular momentum along the short“s-axis”, and the hole-like nucleon tends to align their angular momentum along the long“l-axis”. The total angular momentum will be aplanar, i.e. tilting away from any principal axes and from a plane defined by any two of three principal axes. The system formed by the three mutually perpendicular angular momenta contains left-handed and right-handed geometrical configurations. In the intrinsic body-fixed frame, chiral symmetry is broken. In the laboratory frame, the restoration of the chiral symmetry results in two bands which are of the same parity and almost degenerate in energy.
A great number of experimental and theoretical studies have suggested some fingerprints of nuclear chiral bands. These fingerprints are as follows:
1. The degenerate bands of the same parity, connected to each other via M1/E2 transitions.
2. The bands should show a smooth variation of the energy staggering parameter S(I), defined as S(I)=[E(I)-E(I-1)]/2I.
3. The stronger intraband M1 transitions and the weak E2 linking transitions at high spin states.
4. The staggering interband B(M1)/B(E2) ratios of the partner bands with spin. In the A~100 mass region, the chiral bands are built on theπh11/2?νh11/2 configuration, the odd spin values are staggered lower compared to even spin values. In the A~130 mass region, the chiral bands are built on theπg9/2?νh11/2 positive parity configuration, the staggering phase is opposite.
5. The electromagnetic transition probabilities should be similar in chiral bands. The absolute B(M1) and B(E2) transition probabilities are critical for the identification of the chiral bands.
The purpose of this thesis is to extract the absolute B(M1) and B(E2) transition probabilities of the chiral bands in 130Cs by the lifetime measurements using Doppler Shift Attenuation Method (DSAM) to test whether the electromagnetic transition rates fulfill the fingerprint of the ideal chiral geometry. The odd-odd nucleus 130Cs, with 55 protons and 75 neutrons, has two valence nucleons outside theγ-soft 128Xe core. The PES (Potential Energy Surface) calculation shows that the valence proton lies in the h11/2[550]1/2- orbital and the valence neutron lies in the h11/2[514]9/2- orbital. The opposite shape-driving effects of the particle-like proton and the hole-like neutron result in the stable triaxial deformation in 130Cs. The TRS (Total Routhian Surface) calculation also confirms the conclusion, i.e.β=0.18、γ=27°. The high spin states of 130Cs have been investigated by T.Kokie and P.Joshi. The near-degenerateΔI=1 double bands with the same positive parity have been observed.
In the present work, the high spin states of 130Cs were populated via the reaction of 124Sn(11B, 5n)130Cs at the beam energy of 65 MeV. The 11B beam was delivered by the HI-13 tandem accelerator at the China Institute of Atomic Energy (CIAE). The target consisted of a 7.06 mg/cm2 thick 124Sn backed on lead of 6.7mg/cm2 thickness in order to slow down and stop the recoiling nuclei. Theγ-γcoincidence events were collected by an array of 14 HPGe detectors with BGO Compton suppression shield. A total of about 220×106 coincidence events were collected. Theγ-γcoincidence events were sorted into several conventional two-dimensional matrices and analyzed using the RADWARE package base on Linux-PC system.
From theγ-γcoincidence analysis, the same scheme of 130Cs as before has been reproduced in this experiment. Level lifetimes have been measured using DSAM. The Doppler Broadened peak shapes of the forward and backward angle detectors with respect to the beam axis were obtained. The stopping powers of atoms were calculated to get velocity change information of the beam and recoil nuclei traversing the target and the backing material. Electronic stopping powers were calculated with the LSS-theory and the nuclear stopping powers were used according to Ziegler et al. The velocity profile of recoiling nuclei was simulated by the Monte Carlo procedure. The line shapes ofγ-transitions are analyzed by the DSAMFT code of Gascon. Lifetime analysis was performed starting from the highest energy level. The lifetimes of seven states in yrast band and four states in side band have been determined. The best fittings were obtained on the basis of a minimization of the reducedχ2.
The absolute B(M1) and B(E2) transition probabilities have been derived from the measured lifetimes. Comparison with the chiral bands, the experimental B(M1) and B(E2) values are essentially the same from the spin 14+ to 17+ in the experimental uncertainties. With the increasing spin in the chiral bands, the B(E2) values remain constant; the B(M1) values show the character of staggering, and the B(M1) values of transitions depopulating the odd spin levels are larger than that of even spin; the B(M1) values of interband transitions show the opposite odd-even spin staggering phase, and the B(M1) values of even spin are larger than those of odd spin. The main features of the experimental results support the identification of chiral partner bands.
For the purpose of the current study, the Particle-Rotor Model (PRM) with one particle and one hole coupled with a triaxial rotor has been developed and used due to its advantages of the good angular momentum number and simple picture. PRM is a quantum mechanical method that describes the system in the laboratory framework and yields directly the energy splitting and tunneling between doublet bands. The excited energy spectra and the transitional probabilities of the chiral bands have been calculated. The results support the chiral bands in 130Cs. At low spins, total angular momentum is mainly contributed by the valence nucleons and remains in the plane spanned by the short and long axes. This situation can be called as weak chiral symmetry broken, and the energy splitting is large. In the spin interval of 12+≤I≤18+, with the increasing of the collective angular momentum, the rotation becomes the chiral rotation, energy of the rotational bands begin degenerate. With the increasing of rotation frequency, the particles alignments along with medium axis, contributions from the valence particle and hole become negligible compared with the total spin, the nuclei rotation becomes the axial rotation.
From the comparison of the experimental and the theoretical results, it can be seen that the agreement is excellent for the excited energy at high spin region. The magnitude, staggering, and the changing trend of electromagnetic transition rates are reproduced quite well. The experimental B(M1) odd-even staggering phase is reproduced in the PRM calculation, i.e., the values at odd spins are larger than those of even spins in intraband and the values at odd spins are smaller than those of even spins in the interband.
To further confirm the picture of chirality in 130Cs, the orientation of the angular momentum for the rotor as well as the valence proton and neutron are calculated for the yrast band and side band. The effective angles in body frame are also investigated. In a large spin interval of 9+≤I≤18+, the effective angles are larger than 45°. This behavior suggests a remarkable aplanar rotation in this nucleus. With respect to the high-spin states (I≥14+),The effective angles show the odd-even staggering pattern, which indicates quantum tunneling between the left-handed and right-handed system. As the total angular moment I increases, the effective angles gradually decrease and reach a constant. This behavior of the effective angles suggests that the angular momentum align along the same direction at high spin. The probability distributions for the l.i.s axes projections of the total angular momentum have been calculated. The results indicate the partner bands of 130Cs shows clearly the characteristics of static chirality at the higher spin.
A systematic comparison of the candidate chiral bands in A～130 mass region has been performed. The near degenerateΔI=1 positive parity bands in odd-odd 122-132Cs isotopes have been studied. The comparisons of the excited energy, signature splitting, B(M1)/B(E2) ratios, and TRS calculations show the partner bands in the 126.128.130Cs fulfill the picture of chiral bands. The absolute electromagnetic transition probabilities of the measured level lifetimes in several candidate chiral bands have been systematic analyzed.
The level lifetimes in 129Cs have been measured. The quadrupole moments of three bands have been deduced. The experimental results indicate that the Qt values of the negative parity band are smaller than those of the positive parity bands, probably due to the differentγ-deformation driving effects of different proton orbital. The Qt values exhibit a considerable change near the band crossing region in these bands. This behavior demonstrates that nuclear shape changing results from the neutron or proton alignments.
As a conclusion, the level lifetimes of chiral band in 130Cs have been determined using DSAM. The absolute B(M1) and B(E2) transition probabilities were derived. The PRM calculations were performed and the results agree with the experimental results, which indicates the chiral bands of this nucleus in spin interval of 14+≤I≤17+. Systematic comparison and analysis of candidate chiral bands in A～130 mass region has been performed. The level lifetimes in 129Cs have been measured. The nuclear shapes of three bands have been investigated.
130Cs核芯具有软的γ形变;核芯外的价质子位于高j低Ω轨道,具有粒子特性;而价中子位于高j高Ω轨道,具有空穴特性。两种不同特性的价核子具有相反的形状驱动效应,导致130Cs具有稳定的三轴形变。TRS计算结果也显示130Cs核具有较大的三轴形变满足产生手征双重带的条件。实验重建了130Cs的候选手征双重带,测量能级寿命,提取了电磁跃迁几率。对130Cs候选手征双重带的激发能、旋称劈裂、约化电磁跃迁几率比、绝对电磁跃迁几率进行了比较分析,实验结果表明130Cs的候选手征双重带具有能量近似简并的能级;旋称劈裂较小而且随自旋的变化平滑;约化跃迁几率比表现出明显的奇偶自旋振荡;具有相近的绝对电磁跃迁几率值,较小的B(E2)值和B(M1)值典型的奇偶自旋振荡。利用PRM理论模型计算了130Cs手征双重带的激发能和电磁跃迁几率,在较高自旋处理论计算很好的再现了实验结果。对核芯、价质子、价中子三个角动量间的有效角度以及总角动量在三个主轴投影分布几率进行了计算,计算结果表明在较高自旋处130Cs表现出静态手征特性。
论文对A-130区的候选手征双重带进行了分析。122-132Cs的系统分析认为在126-130Cs奇奇核的候选手征双重带具有好的手征特性。还对已经提取能级寿命的候选手征双重带的电磁跃迁几率进行了分析,分析显示该核区的手征双重带具有较小的B(E2)值和典型的B(M1)值奇偶自旋振荡。对于该核区的能级近简并的伙伴带不一定是手征双重带。
测量了129Cs的三条主要转动带的能级寿命,提取了电四极矩值。实验结果指出,πh11/2组态的转动带的电四极矩值小于πg7/2和πd5/2转动带,这可能主要是由于不同质子轨道的三轴形变驱动效应不同导致;在较高自旋处三个带的Qt值出现明显的变化,这主要来至于h11/2质子或中子的顺排。
Chiral symmetry exists commonly in nature. Since the chiral symmetry broken in triaxial-deformed nuclei has been predicted by Frauendorf and Meng in 1997, nuclear chiral structure has attracted significant interest of both theoretical and experimental studies. More than 20 candidate chiral bands with the same parity and degenerate energy have been reported in odd-odd, odd-A, and even-even nuclei of the A~100,130,190 mass regions in experiments. The cores in these nuclei are soft toγ-deformation;, the proton (or neutron) Fermi surface lies in the high-j low-Ωorbital (particle-like), and the neutron (or proton) Fermi surface is located in the middle or upper of high-j subshell (hole-like). These nuclei are suggested to have stable triaxial deformation due to the different deformation-driving effects of the hole-like and particle-like valence nucleons. In the triaixal-deformed nuclei, the core’s collective angular momentum will favour alignment with the intermediate“i-axis”, which has the largest moment of inertia. The particle-like nucleon tends to align their angular momentum along the short“s-axis”, and the hole-like nucleon tends to align their angular momentum along the long“l-axis”. The total angular momentum will be aplanar, i.e. tilting away from any principal axes and from a plane defined by any two of three principal axes. The system formed by the three mutually perpendicular angular momenta contains left-handed and right-handed geometrical configurations. In the intrinsic body-fixed frame, chiral symmetry is broken. In the laboratory frame, the restoration of the chiral symmetry results in two bands which are of the same parity and almost degenerate in energy.
A great number of experimental and theoretical studies have suggested some fingerprints of nuclear chiral bands. These fingerprints are as follows:
1. The degenerate bands of the same parity, connected to each other via M1/E2 transitions.
2. The bands should show a smooth variation of the energy staggering parameter S(I), defined as S(I)=[E(I)-E(I-1)]/2I.
3. The stronger intraband M1 transitions and the weak E2 linking transitions at high spin states.
4. The staggering interband B(M1)/B(E2) ratios of the partner bands with spin. In the A~100 mass region, the chiral bands are built on theπh11/2?νh11/2 configuration, the odd spin values are staggered lower compared to even spin values. In the A~130 mass region, the chiral bands are built on theπg9/2?νh11/2 positive parity configuration, the staggering phase is opposite.
5. The electromagnetic transition probabilities should be similar in chiral bands. The absolute B(M1) and B(E2) transition probabilities are critical for the identification of the chiral bands.
The purpose of this thesis is to extract the absolute B(M1) and B(E2) transition probabilities of the chiral bands in 130Cs by the lifetime measurements using Doppler Shift Attenuation Method (DSAM) to test whether the electromagnetic transition rates fulfill the fingerprint of the ideal chiral geometry. The odd-odd nucleus 130Cs, with 55 protons and 75 neutrons, has two valence nucleons outside theγ-soft 128Xe core. The PES (Potential Energy Surface) calculation shows that the valence proton lies in the h11/2[550]1/2- orbital and the valence neutron lies in the h11/2[514]9/2- orbital. The opposite shape-driving effects of the particle-like proton and the hole-like neutron result in the stable triaxial deformation in 130Cs. The TRS (Total Routhian Surface) calculation also confirms the conclusion, i.e.β=0.18、γ=27°. The high spin states of 130Cs have been investigated by T.Kokie and P.Joshi. The near-degenerateΔI=1 double bands with the same positive parity have been observed.
In the present work, the high spin states of 130Cs were populated via the reaction of 124Sn(11B, 5n)130Cs at the beam energy of 65 MeV. The 11B beam was delivered by the HI-13 tandem accelerator at the China Institute of Atomic Energy (CIAE). The target consisted of a 7.06 mg/cm2 thick 124Sn backed on lead of 6.7mg/cm2 thickness in order to slow down and stop the recoiling nuclei. Theγ-γcoincidence events were collected by an array of 14 HPGe detectors with BGO Compton suppression shield. A total of about 220×106 coincidence events were collected. Theγ-γcoincidence events were sorted into several conventional two-dimensional matrices and analyzed using the RADWARE package base on Linux-PC system.
From theγ-γcoincidence analysis, the same scheme of 130Cs as before has been reproduced in this experiment. Level lifetimes have been measured using DSAM. The Doppler Broadened peak shapes of the forward and backward angle detectors with respect to the beam axis were obtained. The stopping powers of atoms were calculated to get velocity change information of the beam and recoil nuclei traversing the target and the backing material. Electronic stopping powers were calculated with the LSS-theory and the nuclear stopping powers were used according to Ziegler et al. The velocity profile of recoiling nuclei was simulated by the Monte Carlo procedure. The line shapes ofγ-transitions are analyzed by the DSAMFT code of Gascon. Lifetime analysis was performed starting from the highest energy level. The lifetimes of seven states in yrast band and four states in side band have been determined. The best fittings were obtained on the basis of a minimization of the reducedχ2.
The absolute B(M1) and B(E2) transition probabilities have been derived from the measured lifetimes. Comparison with the chiral bands, the experimental B(M1) and B(E2) values are essentially the same from the spin 14+ to 17+ in the experimental uncertainties. With the increasing spin in the chiral bands, the B(E2) values remain constant; the B(M1) values show the character of staggering, and the B(M1) values of transitions depopulating the odd spin levels are larger than that of even spin; the B(M1) values of interband transitions show the opposite odd-even spin staggering phase, and the B(M1) values of even spin are larger than those of odd spin. The main features of the experimental results support the identification of chiral partner bands.
For the purpose of the current study, the Particle-Rotor Model (PRM) with one particle and one hole coupled with a triaxial rotor has been developed and used due to its advantages of the good angular momentum number and simple picture. PRM is a quantum mechanical method that describes the system in the laboratory framework and yields directly the energy splitting and tunneling between doublet bands. The excited energy spectra and the transitional probabilities of the chiral bands have been calculated. The results support the chiral bands in 130Cs. At low spins, total angular momentum is mainly contributed by the valence nucleons and remains in the plane spanned by the short and long axes. This situation can be called as weak chiral symmetry broken, and the energy splitting is large. In the spin interval of 12+≤I≤18+, with the increasing of the collective angular momentum, the rotation becomes the chiral rotation, energy of the rotational bands begin degenerate. With the increasing of rotation frequency, the particles alignments along with medium axis, contributions from the valence particle and hole become negligible compared with the total spin, the nuclei rotation becomes the axial rotation.
From the comparison of the experimental and the theoretical results, it can be seen that the agreement is excellent for the excited energy at high spin region. The magnitude, staggering, and the changing trend of electromagnetic transition rates are reproduced quite well. The experimental B(M1) odd-even staggering phase is reproduced in the PRM calculation, i.e., the values at odd spins are larger than those of even spins in intraband and the values at odd spins are smaller than those of even spins in the interband.
To further confirm the picture of chirality in 130Cs, the orientation of the angular momentum for the rotor as well as the valence proton and neutron are calculated for the yrast band and side band. The effective angles in body frame are also investigated. In a large spin interval of 9+≤I≤18+, the effective angles are larger than 45°. This behavior suggests a remarkable aplanar rotation in this nucleus. With respect to the high-spin states (I≥14+),The effective angles show the odd-even staggering pattern, which indicates quantum tunneling between the left-handed and right-handed system. As the total angular moment I increases, the effective angles gradually decrease and reach a constant. This behavior of the effective angles suggests that the angular momentum align along the same direction at high spin. The probability distributions for the l.i.s axes projections of the total angular momentum have been calculated. The results indicate the partner bands of 130Cs shows clearly the characteristics of static chirality at the higher spin.
A systematic comparison of the candidate chiral bands in A～130 mass region has been performed. The near degenerateΔI=1 positive parity bands in odd-odd 122-132Cs isotopes have been studied. The comparisons of the excited energy, signature splitting, B(M1)/B(E2) ratios, and TRS calculations show the partner bands in the 126.128.130Cs fulfill the picture of chiral bands. The absolute electromagnetic transition probabilities of the measured level lifetimes in several candidate chiral bands have been systematic analyzed.
The level lifetimes in 129Cs have been measured. The quadrupole moments of three bands have been deduced. The experimental results indicate that the Qt values of the negative parity band are smaller than those of the positive parity bands, probably due to the differentγ-deformation driving effects of different proton orbital. The Qt values exhibit a considerable change near the band crossing region in these bands. This behavior demonstrates that nuclear shape changing results from the neutron or proton alignments.
As a conclusion, the level lifetimes of chiral band in 130Cs have been determined using DSAM. The absolute B(M1) and B(E2) transition probabilities were derived. The PRM calculations were performed and the results agree with the experimental results, which indicates the chiral bands of this nucleus in spin interval of 14+≤I≤17+. Systematic comparison and analysis of candidate chiral bands in A～130 mass region has been performed. The level lifetimes in 129Cs have been measured. The nuclear shapes of three bands have been investigated.
引文
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[1] Morinaga H and Gugelot P C, Nucl. Phys. 1963 46:210
[2]卢希庭.原子核物理.原子能出版社. 1987
[3]张振龙. 171Ta能级寿命测量.硕士论文.吉林大学. 2003
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[17]杨小青,曹小平. KODAQ数据获取系统用户使用手册.中国原子能科学研究院
[1]复旦大学,清华大学,北京大学.原子核物理实验方法.原子能出版社. 1994
[2]刘颖. 129Ce核旋称劈裂与三轴性研究.博士论文.中国原子能科学研究院. 2008
[3]李立华. 178Os核激发态的寿命测量.硕士论文.中国原子能科学研究院. 2007
[4]吴治华等.原子核物理实验方法.原子能出版社. 1997
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[6] Petkov P, Tonev D,Dewald A et al. Nucl Instrum Methods Phys. Res. 2002 A488:555
[7]仲启平.利用改进后的多普勒偏移方法进行寿命测量来研究134Pr核手征态性质.博士论文.中国原子能科学研究院.
[8] Devons S, Manning G et al. Proceeding of the Physical Society. 1995 A68:18
[9]张振龙. 171Ta能级寿命测量.硕士论文.吉林大学. 2003
[1] Frauendorf S, MENG J. Nucl Phys. 1997 A617:131-147
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[8] Simons A J, Joshi P et al. J Phys. 2005 G31:541-552
[9] Rainovski G, Paul E S et al. Phys Rev 2003 C68:024318
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[18] Vaman C, Fossan D B. et al. Phys Rev Lett. 2004 92:032501
[19] Joshi P, Jenkins D G et al. Phys Lett. 2004 B595:135-142
[20] Joshi P, Carpenter M P et al. Phys Rev Lett. 2007 98:102501
[21] Balabanski D L et al. Phys Rev. 2004 C70:044305
[22] Lawrie E A et al.Phys Rev. 2008 C78:021305(R)
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