Nuclear reactions and the double beta decay

Charge-exchange reactions of (n,p) and (p,n) types at intermediate energies are introduced as a tool for the study of nuclear matrix element in ββ decay. Here, the (n,p) type reactions are realized through , where ²He refers to two protons in a singlet ¹S₀ state and where both of these are momentum analyzed and detected by the same spectrometer and detector. These reactions have been developed and performed exclusively at KVI, Groningen (NL), using an incident deuteron energy of 183 MeV. The  reaction is of (p,n) type and was developed at the RCNP facility in Osaka (JP) at incident energies of 420 MeV. Using both reaction types one can extract the Gamow-Teller transition strengths B(GT⁺) and , which define the two “legs” of the ββ decay matrix elements for the 2νββ decay. The high resolution available in both reactions allows a detailed insight into the excitations of the intermediate odd-odd nuclei and, as will be shown, some unexpected features are being unveiled.     

谐振子径向幂坐标矩阵元的一般递推关系

利用谐振子径向波函数的渐近行为和积分特性,导出了谐振子径向幂坐标矩阵元〈n′_rl′|r~k|n_rl〉的递推关系,从而把有关文献中关于对角元〈n_rl|r~k|n_rl〉的递推关系推广到更为一般的形式。     

Nuclear longitudinal form factors for axially deformed charge distributions expanded by nonorthogonal basis functions

In this paper,the nuclear longitudinal form factors are systematically studied from the intrinsic charge multipoles.For axially deformed nuclei,two different types of density profiles are used to describe their charge distributions.For the same charge distributions expanded with different basis functions,the corresponding longitudinal form factors are derived and compared with each other.Results show the multipoles C_λ of longitudinal form factors are independent of the basis functions of charge distributions.Further numerical calculations of longitudinal form factors of~(12)C indicates that the C_0 multipole reflects the contributions of spherical components of all nonorthogonal basis functions.For deformed nuclei,their charge RMS radii can also be determined accurately by the C_0 measurement.The studies in this paper examine the model-independent properties of electron scattering,which are useful for interpreting electron scattering experiments on exotic deformed nuclei.     

也谈径向矩阵元的递推关系

利用超位力定理及其推广形式给出了一维、二维和三维系统径向矩阵元递推关系的一般表示式,并具体求出了谐振子系统及非相对论氢原子系统中径向矩阵元的递推关系．     

谐振子基在复标度方法中的应用

在利用薛定谔方程求解共振态能量的过程中,成功的将谐振子基应用于复标度方法,求解出共振态的能量公式,并以一个比较成熟的势作为检验势,得出比较精确的结果,也作出共振态能量在复能量坐标系中的能量分布.对其中的两个参数基数N和转动角θ进行讨论与分析,验证了共振态的一个原理:在对共振态的计算过程中,计算参数的改变不会影响共振态的位置.     

谐振子基在复标度方法中的应用

在利用薛定谔方程求解共振态能量的过程中，成功的将谐振子基应用于复标度方法，求 解出共振态的能量公式，并以一个比较成熟的势作为检验势，得出比较精确的结果，也作出共振态能量在复能量坐标系中的能量分布。对其中的两个参数基数N和转动角µ进行讨论与分析，验证了共振态的一个原理：在对共振态的计算过程中，计算参数的改变不会影响共振态的位置。     

均匀磁场中三维各向同性谐振子微扰矩阵元的普遍表达式

根据Laguerre多项式的积分公式,在考虑了哈密顿量中正比于B~2项影响的情况下,导出了均匀磁场中三维各向同性谐振子微扰矩阵元的普遍表达式,并指出n=3能级的简并度完全解除．     

Second harmonic generation in a disk shaped quantum dot in the presence of spin-orbit interaction

The second harmonic generation (SHG) coefficients for a disk shaped quantum dot (DSQD) in the magnetic field are studied in the presence of spin-orbit interactions (SOI). The spin-orbit terms we have used in our calculations are both Rashba and Dresselhaus. We have shown that the presence of SOI modifies the SHG terms. In addition, it has been shown that SOI coupling terms influence the spectrum of DSQD resulting in defined changes in the harmonic generation.     

环形非球谐振子径向矩阵元的通项公式及其递推关系

环形非球谐振子的势能函数为V(r,θ)=12mω2r2+22mAr2+22mbr2sin2θ,其精确的能谱方程和归一化的波函数已经获得.在此基础上,给出了环形非球谐振子径向矩阵元的通项公式和不同幂次径向矩阵元之间所满足的递推关系.作为特例,讨论了球谐振子、非球谐振子和环形振子的有关结果. 关键词： 环形非球谐振子 径向矩阵元 通项公式 递推关系     

一种导出谐振子矩阵元通式的简捷方法

在导出(f(X)+g(P))k正规乘积形式的基础上,利用未归一化的相干态与谐振子的本征态之间的关系计算出的通式,并对所得的结果进行了讨论.本文所用方法显得清晰易懂、推导简捷明快.     

Systematic trends in the line strengths and radial matrix elements of E1 transitions in the Be isoelectronic sequence

Line strengthS and radial matrix elementσ for the dipole allowed transitions withinn=2 complex of ions in the Be isoelectronic sequence have been fitted in the formsZ ² S=A+B/(Z − C) andZσ=A′ + B′/(Z − C′). The constantsA, B, C andA′, B′, C′ have been calculated by employing a non-linear least square method. The relevant data forS andσ have been taken from calculations which includes correlation effects. It is shown that the fitted yalues ofA andA′ are in excellent accord with their hydrogenic values (Z →α) provided that we express the zeroth-order wavefunction of the ground state 1s²2s^{2 1} S as a quantum-mechanical admixture of the Hartree-Fock (HF) state 1s²2s^{2 1} S and the near-degenerate state 1s²2p^{2 1} S.     

一维线性谐振子哈密顿量改写中的非幺正变换

通过引入一非幺正算符实现了对一维线性谐振子系统哈密顿量的从坐标、动量表象(Q,P)到占有数表象(a,a+)的改写.     

Search for Superheavy Elements in the Nature

The existence of relatively stable elements beyond the present Periodic Table is predicted by various theoretical calculations. Considering all experiments of the search for superheavy elements (SHE) in nature and their non definite positive results further search seems to be pessimistic. Nevertheless in this work the scientific necessity to continue the search in nature by a modified manner using industrial enrichment steps is pointed out.     

Search for tensor couplings in the weak interaction

The existence of exotic couplings in the weak interaction can be tested by a precise measurement of the β-ν angular correlation parameter a in nuclear beta decay. In the case of ⁶He, the ratio of tensor and axial-vector couplings can be determined. The goal of the LPC Trap experiment is to improve the limits on the existence of tensor currents. The LPCTrap setup is installed on the low energy beam line LIRAT of the SPIRAL/GANIL facility. The ⁶He⁺ ions are confined in a novel transparent Paul trap allowing the detection in coincidence of both the β-particle and the recoil ion. The detection setup enables to detect the position and energy of these two particles. The a parameter can then be extracted from the time of flight spectrum of the recoil ions. The first ⁶He⁺ decay events were observed in May 2005 during a commissioning run. Over 10⁵ coincidence events have been recorded during a second run in July 2006.     

Nuclear data requirements for accelerator driven sub-critical systems — A roadmap in the Indian context

The development of accelerator driven sub-critical systems (ADSS) require significant amount of new nuclear data in extended energy regions as well as for a variety of new materials. This paper reviews these perspectives in the Indian context.      

Spontaneous-fission decay properties and production cross-sections for the neutron-deficient nobelium isotopes formed in the 44, 48Ca + 204, 206, 208Pb reactions

Heavy-ion fusion reactions ⁴⁸Ca + ²⁰⁴Pb and ⁴⁴Ca + ²⁰⁸Pb leading to the same compound nucleus ²⁵²No^* were run in attempts to produce new neutron-deficient spontaneous-fission isotopes of ^249,250No using the electrostatic separator VASSILISSA. Production cross-sections for the spontaneous-fission activities with the half-lives 5.6 and 54 μs observed in these reactions are compared with the measured ones for the well-known isotopes of ^{251 - 255}No formed in the heavy-ion fusion reactions ⁴⁸Ca + ²⁰⁶Pb and ⁴⁸Ca + ²⁰⁸Pb. The obtained excitation functions for the reaction products formed after the evaporation of 1-4 neutrons from the corresponding compound No nuclei have been compared with similar data obtained earlier and results of statistical model calculations. Received: 26 July 2002 / Accepted: 5 November 2002 / Published online: 18 March 2003 RID="a" ID="a"e-mail: eremin@sunvas.jinr.ru Communicated by J. ?yst?     

Electric and magnetic response to the continuum for A = 7 isobars in a dicluster model

The mirror isobars ⁷Li and ⁷Be are investigated in a dicluster model. The magnetic dipole moments and the magnetic dipole response to the continuum are calculated in this framework. The magnetic contribution is found to be small with respect to electric dipole and quadrupole excitations even at astrophysical energies, at a variance with the case of the deuteron. Energy-weighted molecular sum rules are evaluated and a formula for the molecular magnetic dipole sum rule is found which matches the numerical calculations. Cross-sections for photo-dissociation and radiative capture as well as the S -factor for reactions of astrophysical significance are calculated with good agreement with known experimental data.     

Coincidence Doppler shift lifetime measurements in 73,74Se and 74Br using the EUROBALL Cluster cube array

Subpicosecond lifetimes of high spin states in the rotational nuclei ⁷³Se, ⁷⁴Se and ⁷⁴Br have been measured using the ⁵⁸Ni +¹⁹F compound reaction and the Doppler Shift Attenuation method. Six EUROBALL Cluster detectors arranged in cube geometry allowed us to select the relevant transitions in γγ coincidence mode. The high counting statistics achieved in this setup also facilitated the determination of average sidefeeding times, which were found to agree rather well with the results of Monte-Carlo calculations of the particle and γ-ray evaporation process. The deduced quadrupole strengths and deformations are compared with the results of previous measurements and the predictions of Cranked Shell Model calculations. In ⁷⁴Br, a large and constant prolate deformation of β₂= 0.37(1) was found for the presumed 4⁺ and 3⁻ two-quasiparticle bands. Received: 2 July 1999     

Nuclear deformation and the two-neutrino double- β decay in <Superscript>124, 126</Superscript>Xe , <Superscript>128, 130</Superscript>Te , <Superscript>130, 132</Superscript>Ba and <Superscript>150</Superscript>Nd isotopes

The two-neutrino double-beta decay of ^{124, 126}Xe , ^{128, 130}Te , ^{130, 132}Ba and ¹⁵⁰Nd isotopes is studied in the Projected Hartree-Fock-Bogoliubov (PHFB) model. Theoretical 2ν β^-β^- half-lives of ^{128, 130}Te , and ¹⁵⁰Nd isotopes, and 2ν β⁺β⁺ , 2ν β⁺ EC and 2ν ECEC for ^{124, 126}Xe and ^{130, 132}Ba nuclei are presented. Calculated quadrupolar transition probabilities B(E2 : 0⁺ → 2⁺) , static quadrupole moments and g -factors in the parent and daughter nuclei reproduce the experimental information, validating the reliability of the model wave functions. The anticorrelation between nuclear deformation and the nuclear transition matrix element M _2ν is confirmed.