Spin structures of the ground states of four body bound systems with spin 3 cold atoms

We consider the case that four spin-3 atoms are confined in an optical trap. The temperature is so low that the spatial degrees of freedom have been frozen. Exact numerical and analytical solutions for the spin-states have been both obtained. Two kinds of phase-diagrams for the ground states (g.s.) have been plotted. In general, the eigen-states with the total-spin S (a good quantum number) can be expanded in terms of a few basis-states $$f_{S,i}$$ f S , i . Let $$P_{f_{S,i}}^{\lambda }$$ P f S , i λ be the probability of a pair of spins coupled to $$\lambda =0, 2, 4$$ λ = 0 , 2 , 4 , and 6 in the $$f_{S,i}$$ f S , i state. Obviously, when the strength $$g_{\lambda }$$ g λ of the $$\lambda $$ λ -channel is more negative, the basis-state with the largest $$P_{f_{S,i}}^{\lambda }$$ P f S , i λ would be more preferred by the g.s.. When two strengths are more negative, the two basis-states with the two largest probabilities would be more important components. Thus, based on the probabilities, the spin-structures (described via the basis-states) can be understood. Furthermore, all the details in the phase-diagrams, say, the critical points of transition, can also be explained. Note that, for $$f_{S,i}$$ f S , i , $$P_{f_{S,i}}^{\lambda }$$ P f S , i λ is completely determined by symmetry. Thus, symmetry plays a very important role in determining the spin-structure of the g.s..

Nonstatistical Reaction Dynamics

Nonstatistical dynamics is important for many chemical reactions. The Rice-Ramsperger-Kassel-Marcus (RRKM) theory of unimolecular kinetics assumes a reactant molecule maintains a statistical microcanonical ensemble of vibrational states during its dissociation so that its unimolecular dynamics are time independent. Such dynamics results when the reactant's atomic motion is chaotic or irregular. Intrinsic non-RRKM dynamics occurs when part of the reactant's phase space consists of quasiperiodic/regular motion and a bottleneck exists, so that the unimolecular rate constant is time dependent. Nonrandom excitation of a molecule may result in short-time apparent non-RRKM dynamics. For rotational activation, the 2J + 1 K levels for a particular J may be highly mixed, making K an active degree of freedom, or K may be a good quantum number and an adiabatic degree of freedom. Nonstatistical dynamics is often important for bimolecular reactions and their intermediates and for product-energy partitioning of bimolecular and unimolecular reactions. Post–transition state dynamics is often highly complex and nonstatistical.

Goodness of Generalized Seniority in Even-even Sn Isotopes.

Seniority has proved to be a unique and simple probe to address some of the complex issues underlying nuclear structure of nuclei close to magic numbers. An extension from the concept of seniority in single-j shell to generalized seniority in multi-j shell has recently been provided by us. We have, consequently, established new selection rules for gamma decays and discovered the new seniority isomers decaying via odd electric multipole operators. We have successfully explained the B(EL; L=1,2,3) behavior of various high spin isomers and other excited states. More specifically, we have been able to explain the long-standing puzzle of double hump in the B(E2) values for the first excited 2+ states of even-even Z=50 (Sn) isotopes. In the present paper, we review these generalized seniority calculations with emphasis on even-even Sn isotopes. We first discuss the generalized seniority results for the E1 decaying 13- isomers and E2 decaying 10+, 15- isomers, and then present the cases of first-excited 2+ and 3- states. The generalized seniority proves out to be a reasonably good quantum number. The significance of configuration mixing is found to be true. The calculated results has been validated till high seniority v=4 states and expected to be valid for higher seniority v=6,… states also.

Manifestations of isospin in nearest neighbor spacing distributions for the f-p model space

The strong interactions are charge independent. If we limit ourselves to the strong interactions, we have the isospin [Formula: see text] as a good quantum number. Here, we consider the lack of level repulsion of states of different isospin and how this effect manifests in nearest neighbor spacing (NNS) histograms, which provide a visual and statistical context in which to study distributions of energy level spacings. In particular, we study nucleons in the [Formula: see text] model space for the nucleus [Formula: see text]. We also compare NNS distributions produced in the isospin formalism to distributions produced in the proton–neutron formalism.

Determination of GT-transition Strengths in \(A=34\) Isobars Using Charge Exchange \((^3\text{He},t)\) Reaction

Under the assumption that isospin \(T\) is a good quantum number, mirror transitions \(T_{z }= +1 \to 0\) and \(T_{z }= -1 \to 0\) were studied in \(A = 34\) isobars, where \(T_{z}\) is \(z\) component of iospin \(T\) and is defined by \(T_{z} = (N-Z)/2\). With a high energy resolution of 35 keV in \(^{34}\)S\((^{3}He,t)^{34}\)Cl reaction measurement at \(0^{\circ}\) scattering angle and at an incident energy of 140 MeV/nucleon, strengths of Fermi and Gamow-Teller (GT) transitions from the \(J^{\pi } = 0^{ + }\), \(T_{z }= +1\) ground state of \(^{34}\)S to the \(J^{\pi } = 1^{+ }\), \(T_{z }= 0\) excited states in \(^{34}\)Cl were determined up to excitation energy \((E_{x})\) of \(7.08\) MeV. The corresponding isospin-symmetric transitions connecting \(T_{z }= -1\) and \(T_{z }= 0\) states can be studied in the \(^{34}\)Ar \(\beta ^{ + }\) decay. The strengths of the \((GT)_{\pm }\) transitions were compared up to the excitation energy of 3.1 MeV. A good agreement was observed for two strong transitions to \(2.580\) MeV and \(3.129\) MeV states, while a disagreement about \(45\text{%}\) was observed for a weaker transition to \(0.666\) MeV low-lying state.

Tz = ±1 → 0 ISOSPIN SYMMETRY GAMOW-TELLER TRANSITIONS IN pf-SHELL NUCLEI

Studying the Gamow-Teller (GT) transitions of stable as well as unstable pf-shell nuclei is one of the key issues in nuclear and astro-nuclear physics. Under the assumption that isospin T is a good quantum number, symmetry is expected for mirror nuclei and the GT transitions starting from the mirror nuclei. We study the GT transitions starting from Tz = ±1 mirror nuclei, respectively, by means of hadronic (3 He , t) charge-exchange reactions and complementary β decays.

Dipole States in 86Sr, 88Sr and 90Zr

A shell model method for calculating dipole states in N > Z even nuclei is discussed. By assuming isospin to be a good quantum number, the spectrum resolves into two classes of states differing in isospin. Applications of this model to 88Sr and 90Zr essentially differ from previous calculations by the use of a new realistic force in the residual interaction. Dipole states in 86Sr are also investigated along with the effect of correlating the ground state wavefunction