在相对论平均场框架内研究软化对称能对核性质的影响及砹缺中子同位素的形状共存
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摘要
本论文在相对论平均场的框架内研究了核物质对称能的软化对有限核基态性质和巨共振的影响以及砹缺中子同位素的形状共存。
对称能和它的密度依赖性对远离β稳定线的同位旋极端不对称核，天体物理等方面有重要作用。鉴于目前对核物质对称能的密度依赖性不是很清楚，甚至在饱和密度处的对称能的取值也不是很确切。我们在相对论平均场模型中，采用包含有混合的同位旋标量-矢量非线性耦合项的拉格朗日密度，它可以“软化”对称能，但不会改变对称核物质在饱和点的性质。为保持原有参数，我们采用了一种简单的方案，保持在平均密度约0.1fm~(-3)处的对称能固定不变：对称能的密度依赖性发生改变，计算求得实验上已精确测量的核~(208)Pb的电荷半径和结合能等不改变，只是中子半径，因而中子皮的厚度发生改变。研究了Ca丰中子核的基态性质对对称能的密度依赖性的敏感性。随着对称能的软化，中子的中心密度增加，而质子的密度基本维持不变。因而，中子皮的厚度变小；而且，随着中子数的增多，中子的中心密度增加越显著。这意味着中子数越多，中子皮的厚度改变越大，对称能的密度依赖性影响增强。研究了Ca丰中子核中子皮的厚度与核物质对称能的关联，结果表明，中子皮的厚度几乎线性依赖饱和密度处的对称能。讨论了Ca丰中子核中子单粒子态对对称能的密度依赖性的敏感性。发现中子单粒子能级及其均方根半径与核物质对称能的密度依赖性相关。Ca同位素丰中子核的中子单粒子轨道由于对称能的软化被“压缩”，因而核的中子均方根半径及中子皮的厚度减小；处在核内部位置束缚单粒子态能量绝对值变大，而束缚松散的单粒子态的结合能绝对值变小。结果，核子的平均结合能基本保持不变。
我们还进一步研究了~(208)Pb中子皮的厚度对高阶核子-ω-ρ介子耦合的敏感性。计算表明，这种同位旋相关的高阶耦合项能够进一步软化对称能，而且能够在不影响其它基态可观测量，如电荷半径(或者质子半径)、结合能的情况下，进一步减小~(208)Pb的中子半径。
我们在建立在相对论平均场基态上一致性的相对论无规位相近似的框架内，通过引进包含有混合的同位旋标量-矢量非线性耦合项的有效拉格朗日密度，讨论了核物质对称能的软化对同位旋标量巨单极共振(ISGMR)的影响。发现由于对称能的软化，计算所得的ISGMR的中心能量变大。通过比较核~(208)Pb，~(144)Sm，~(116)Sn和~(90)Zr实验和计算的巨单极共振能量，给出了核物质不可压缩系数的取值范围。研究表明，有限核的ISGMR能量不仅依赖于核物质的不可压缩性系数，而且与核物质对称能密切相关。发现在巨单极共振的中心能量与核物质的饱和密度处的对称能之间存在线性关联。比较相对论无规位相近似理论计算的ISGMR的中心能量与实验测量值，发现对应于太大或太小不可压缩性系数的参数组，象TM1(K_(nm)=281 MeV)及NLC(K_(nm)=225MeV)，均不能在合理的对称能范围内，再现巨单极共振能量的实验测量值。而象参数组NL3及NLBA，对应的不可压缩性系数约在240-270 MeV，则可以在合理的对称能范围内再现实验值。
此外，我们还研究了Ni同位素偶-偶核的同位旋矢量巨偶极共振和矮共振。讨论了同位旋矢量巨偶极共振，矮共振与中子皮、对称能的关联。发现Ni同位素链的同位旋矢量巨偶极共振的中心能量与中子皮的厚度密切相关：通过同位旋标量-矢量非线性耦合强度的改变，改变中子皮厚度，对矮共振(PDR)中心能量影响很小。这是因为低能矮共振主要是几个价中子相对核芯的振动的贡献，在我们的研究中，采用了保持平均密度处对称能不变的假定，这样对价中子分布的改变很小，因而，在这种模型下对PDR的影响很小。
最后，我们还用轴对称形变相对论平均场方法，采用四极约束方案，在一个大四极形变范围内，计算了At缺中子同位素从质量数A=190到207的能量曲面。发现每个核的能量面都有几个极小值。讨论了形状共存、形状跃迁及四极形变。研究表明，形状共存与质子闯入态Ωπ=13／2~+的占有有关。
The effect of the softening of the symmetry energy of nuclear matter on the ground state properties and giant resonance of finite nuclei as well as the shape coexistence in neutron-deficient At isotopes are studied in relativistic mean field theory.
The symmetry energy and it's density dependence is important to the study of the nuclei which are farther away fromβstable line and depart from equal numbers of neutrons and protons extremely, as well as astrophysics and so on. Since the density dependence of the symmetry energy is poorly known, even the symmetry energy at saturation density is not well constrained experimentally. In view of this, an additional mixed isoscalar-isovector nonlinear coupling term has been adopted in the model Lagrangian in the framework of relativistic mean field theory, which can soften the symmetry energy without affecting the saturation properties of symmetric nuclear matter as the expectation value of the rho-meson field is identically zero. As a simple prescription, we keep the symmetry energy fixed at an average density of 0.1 fm~(-3), which produces a nearly constant proton radius and binding energy for the nucleus ~(208)Pb , both of them are accurately determined experimentally; only the neutron radius, and as a consequence, the neutron skin thickness is modified. The sensitivity of the ground-state properties of neutron-rich Ca isotopes to the density dependence of the symmetry energy is studied. Neutron central density increases with the softening of the symmetry energy, while the proton density essentially remains unchanged; therefore the neutron skin (thickness) S becomes smaller; and the larger the neutron number N, the more prominent the increase of the neutron central density is. This may suggest the larger the neutron number N, the larger the change of the neutron skin S is. In addition, the linear correlation between the neutron skin and the symmetry energy at the saturation density is found. The sensitivity of neutron single particle states in Ca isotopes to the density dependence of the symmetric energy is also investigated. All neutron single orbitals are compressed in each nucleus with the softening of the symmetry energy; therefore, the neutron radius and also the neutron skin decrease. The deeply bound single particle states become deeper, while those loosely bound states become looser. As a result, the binding energy per nucleon remains unchanged.
Furthermore, the relativistic mean field model is supplemented with an additional high order nucleon-ω-ρcoupling term again, and the sensitivity of the neutron skin in ~(208)Pb to this additional term is studied. Calculations show that the high order nucleon-ω-ρcorrection can further soften the symmetry energy, and thus can further decrease the neutron radius of ~(208)Pb without affecting other ground-state observables.
The effect of the softening of the symmetry energy on the isoscalar giant monopole resonance (ISGMR ) is discussed in the framework of a fully consistent relativistic random phase approximation ( RRPA ), based on the effective Lagrangian with the mixed isoscalar-isovector nonlinear coupling term. The calculated Centroid energies of the ISGMR become larger due to the softening of the symmetry energy. A predicted value of the nuclear matter incompressibility coefficient is given by comparison between experimental and calculated energies of the ISGMR in ~(208)Pb, ~(144)Sm, ~(116)Sn and ~(90)Zr. The Centroid energies of the ISGMR of finite nuclei not only depend on the nuclear matter incompressibility coefficient, but also are related to the symmetry energy. It is found that there is a linear correlation between the Centroid energy of the ISGMR and the symmetry energy at saturation density. The RRPA calculation by using parameter sets NL3 or NLBA with the incompressibility K_(nm) around 240-270 MeV can reproduce the experimental ISGMR energy with a reasonable symmetry energy, those parameter sets TM1 ( K_(nm)=281MeV ) and NLC ( K_(nm)=225MeV ) with too large or too small incompressibility could not.
Moreover, correlations between the isovector giant dipole resonance, the Pygmy dipole resonance ( GDR and PDR, respectively) and the symmetry energy, the neutron skin thickness in Ni even-even isotopes are investigated. The Centroid energy of the GDR is related to the variation of the neutron skin obtained by softening the symmetry energy; in contrast, that of the PDR is insensitive to that variation. It is related to the fact that the Pygmy resonance results from the excess neutrons oscillating out of phase with a core composed of equal number of protons and neutrons; and we assume the symmetry energy at the average density fixed, which has little effect on the density distribution of the excess neutrons; therefore, there is little effect on the Pygmy resonance.
Finally, the energy surfaces are calculated for neutron-deficient At isotopes from the mass numbers A=190 to 207 with an axially deformed relativistic mean field approach, using a quadratic constraint scheme in a wide range of quadrupole deformations. There are several minima in the energy surface for each nucleus. The shape-coexistence, shape transition and quadrupole deformation are discussed. The shape-coexistence is associated with the occupation of the occupation the proton intruder stateΩ~π= 13/2~+ in At isotopes.
对称能和它的密度依赖性对远离β稳定线的同位旋极端不对称核，天体物理等方面有重要作用。鉴于目前对核物质对称能的密度依赖性不是很清楚，甚至在饱和密度处的对称能的取值也不是很确切。我们在相对论平均场模型中，采用包含有混合的同位旋标量-矢量非线性耦合项的拉格朗日密度，它可以“软化”对称能，但不会改变对称核物质在饱和点的性质。为保持原有参数，我们采用了一种简单的方案，保持在平均密度约0.1fm~(-3)处的对称能固定不变：对称能的密度依赖性发生改变，计算求得实验上已精确测量的核~(208)Pb的电荷半径和结合能等不改变，只是中子半径，因而中子皮的厚度发生改变。研究了Ca丰中子核的基态性质对对称能的密度依赖性的敏感性。随着对称能的软化，中子的中心密度增加，而质子的密度基本维持不变。因而，中子皮的厚度变小；而且，随着中子数的增多，中子的中心密度增加越显著。这意味着中子数越多，中子皮的厚度改变越大，对称能的密度依赖性影响增强。研究了Ca丰中子核中子皮的厚度与核物质对称能的关联，结果表明，中子皮的厚度几乎线性依赖饱和密度处的对称能。讨论了Ca丰中子核中子单粒子态对对称能的密度依赖性的敏感性。发现中子单粒子能级及其均方根半径与核物质对称能的密度依赖性相关。Ca同位素丰中子核的中子单粒子轨道由于对称能的软化被“压缩”，因而核的中子均方根半径及中子皮的厚度减小；处在核内部位置束缚单粒子态能量绝对值变大，而束缚松散的单粒子态的结合能绝对值变小。结果，核子的平均结合能基本保持不变。
我们还进一步研究了~(208)Pb中子皮的厚度对高阶核子-ω-ρ介子耦合的敏感性。计算表明，这种同位旋相关的高阶耦合项能够进一步软化对称能，而且能够在不影响其它基态可观测量，如电荷半径(或者质子半径)、结合能的情况下，进一步减小~(208)Pb的中子半径。
我们在建立在相对论平均场基态上一致性的相对论无规位相近似的框架内，通过引进包含有混合的同位旋标量-矢量非线性耦合项的有效拉格朗日密度，讨论了核物质对称能的软化对同位旋标量巨单极共振(ISGMR)的影响。发现由于对称能的软化，计算所得的ISGMR的中心能量变大。通过比较核~(208)Pb，~(144)Sm，~(116)Sn和~(90)Zr实验和计算的巨单极共振能量，给出了核物质不可压缩系数的取值范围。研究表明，有限核的ISGMR能量不仅依赖于核物质的不可压缩性系数，而且与核物质对称能密切相关。发现在巨单极共振的中心能量与核物质的饱和密度处的对称能之间存在线性关联。比较相对论无规位相近似理论计算的ISGMR的中心能量与实验测量值，发现对应于太大或太小不可压缩性系数的参数组，象TM1(K_(nm)=281 MeV)及NLC(K_(nm)=225MeV)，均不能在合理的对称能范围内，再现巨单极共振能量的实验测量值。而象参数组NL3及NLBA，对应的不可压缩性系数约在240-270 MeV，则可以在合理的对称能范围内再现实验值。
此外，我们还研究了Ni同位素偶-偶核的同位旋矢量巨偶极共振和矮共振。讨论了同位旋矢量巨偶极共振，矮共振与中子皮、对称能的关联。发现Ni同位素链的同位旋矢量巨偶极共振的中心能量与中子皮的厚度密切相关：通过同位旋标量-矢量非线性耦合强度的改变，改变中子皮厚度，对矮共振(PDR)中心能量影响很小。这是因为低能矮共振主要是几个价中子相对核芯的振动的贡献，在我们的研究中，采用了保持平均密度处对称能不变的假定，这样对价中子分布的改变很小，因而，在这种模型下对PDR的影响很小。
最后，我们还用轴对称形变相对论平均场方法，采用四极约束方案，在一个大四极形变范围内，计算了At缺中子同位素从质量数A=190到207的能量曲面。发现每个核的能量面都有几个极小值。讨论了形状共存、形状跃迁及四极形变。研究表明，形状共存与质子闯入态Ωπ=13／2~+的占有有关。
The effect of the softening of the symmetry energy of nuclear matter on the ground state properties and giant resonance of finite nuclei as well as the shape coexistence in neutron-deficient At isotopes are studied in relativistic mean field theory.
The symmetry energy and it's density dependence is important to the study of the nuclei which are farther away fromβstable line and depart from equal numbers of neutrons and protons extremely, as well as astrophysics and so on. Since the density dependence of the symmetry energy is poorly known, even the symmetry energy at saturation density is not well constrained experimentally. In view of this, an additional mixed isoscalar-isovector nonlinear coupling term has been adopted in the model Lagrangian in the framework of relativistic mean field theory, which can soften the symmetry energy without affecting the saturation properties of symmetric nuclear matter as the expectation value of the rho-meson field is identically zero. As a simple prescription, we keep the symmetry energy fixed at an average density of 0.1 fm~(-3), which produces a nearly constant proton radius and binding energy for the nucleus ~(208)Pb , both of them are accurately determined experimentally; only the neutron radius, and as a consequence, the neutron skin thickness is modified. The sensitivity of the ground-state properties of neutron-rich Ca isotopes to the density dependence of the symmetry energy is studied. Neutron central density increases with the softening of the symmetry energy, while the proton density essentially remains unchanged; therefore the neutron skin (thickness) S becomes smaller; and the larger the neutron number N, the more prominent the increase of the neutron central density is. This may suggest the larger the neutron number N, the larger the change of the neutron skin S is. In addition, the linear correlation between the neutron skin and the symmetry energy at the saturation density is found. The sensitivity of neutron single particle states in Ca isotopes to the density dependence of the symmetric energy is also investigated. All neutron single orbitals are compressed in each nucleus with the softening of the symmetry energy; therefore, the neutron radius and also the neutron skin decrease. The deeply bound single particle states become deeper, while those loosely bound states become looser. As a result, the binding energy per nucleon remains unchanged.
Furthermore, the relativistic mean field model is supplemented with an additional high order nucleon-ω-ρcoupling term again, and the sensitivity of the neutron skin in ~(208)Pb to this additional term is studied. Calculations show that the high order nucleon-ω-ρcorrection can further soften the symmetry energy, and thus can further decrease the neutron radius of ~(208)Pb without affecting other ground-state observables.
The effect of the softening of the symmetry energy on the isoscalar giant monopole resonance (ISGMR ) is discussed in the framework of a fully consistent relativistic random phase approximation ( RRPA ), based on the effective Lagrangian with the mixed isoscalar-isovector nonlinear coupling term. The calculated Centroid energies of the ISGMR become larger due to the softening of the symmetry energy. A predicted value of the nuclear matter incompressibility coefficient is given by comparison between experimental and calculated energies of the ISGMR in ~(208)Pb, ~(144)Sm, ~(116)Sn and ~(90)Zr. The Centroid energies of the ISGMR of finite nuclei not only depend on the nuclear matter incompressibility coefficient, but also are related to the symmetry energy. It is found that there is a linear correlation between the Centroid energy of the ISGMR and the symmetry energy at saturation density. The RRPA calculation by using parameter sets NL3 or NLBA with the incompressibility K_(nm) around 240-270 MeV can reproduce the experimental ISGMR energy with a reasonable symmetry energy, those parameter sets TM1 ( K_(nm)=281MeV ) and NLC ( K_(nm)=225MeV ) with too large or too small incompressibility could not.
Moreover, correlations between the isovector giant dipole resonance, the Pygmy dipole resonance ( GDR and PDR, respectively) and the symmetry energy, the neutron skin thickness in Ni even-even isotopes are investigated. The Centroid energy of the GDR is related to the variation of the neutron skin obtained by softening the symmetry energy; in contrast, that of the PDR is insensitive to that variation. It is related to the fact that the Pygmy resonance results from the excess neutrons oscillating out of phase with a core composed of equal number of protons and neutrons; and we assume the symmetry energy at the average density fixed, which has little effect on the density distribution of the excess neutrons; therefore, there is little effect on the Pygmy resonance.
Finally, the energy surfaces are calculated for neutron-deficient At isotopes from the mass numbers A=190 to 207 with an axially deformed relativistic mean field approach, using a quadratic constraint scheme in a wide range of quadrupole deformations. There are several minima in the energy surface for each nucleus. The shape-coexistence, shape transition and quadrupole deformation are discussed. The shape-coexistence is associated with the occupation of the occupation the proton intruder stateΩ~π= 13/2~+ in At isotopes.
引文
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[72]C．J．Horowitz，and B．D．Serot，Nucl．Pays．A 368，503(1981)．
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[79]J．Pickarewicz，Phys．Rev．C 66，034305(2002)．
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[84]B．L．Berman and S．C．Fultz，Rev．Mod．Phys．47，713(1975)．
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[86]J．Ritman et al．，Phys．Rev．Lett．70，533(1993)．
[87]T．Aumann et al．，Nucl．Phys．A 649，297c(1999)．
[88]N．Ryezayeva et al．，Phys．Rev．Lett．89，272502(2002)．
[89]J．Enders et al．，Nucl．Phys．A 724，243(2003)．
[90]T．Hartmann et al．，Phys．Rev．Lett．93，192501(2004)．
[91]S．Goriely and E．Khan，Nucl．Phys．A 706，217(2002)．
[92]S．Goriely,E．Khan，and M．Samyn，Nucl．Phys．A 739，331(2004)．
[93]D．Vretenar，N．Paar，P．Ring and G．A．Lalazissis，Nucl．Phys．A 692，496(2001)．
[94]N．Paar，D．Vretenar and P．Ring，Phys．Rev．Lett．94，182501(2005)．
[95]J．Piekarewicz，Phys．C 73，044325(2006)．
[96]Z．Y．Ma，H．Toki，B．Q．Chen and N．V．Giai Prog．Theor．Phys．98，917(1997)．
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[102]P．Ring，Y．K．Gambhir，and G．A．Lalazissis，Comput．Phys．Comm．105，77(1997)．
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[110]S．Typel and H．H．Wolter，Nucl．Pays．A 656，331(1999)．
[111]T．Nik(s|ˇ)i(c|′) D．Vretenar，P．Finelli and P．Ring，Phys．Rev．C66，024306(2002)．
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