Wigner Supermultiplet Research Articles

Elementary coupling coefficients for the Wigner supermultiplet symmetry

An algorithm for evaluating Wigner coefficients of U(4) ⊃ SUS(2) ⊗ SUT(2) for the coupling [n14,n24,n34,n44]⊗[1,0,0,0]↓[m14,m24,m34,m44] with arbitrary irreducible representation [n14,n24,n34,n44] is provided based on the algebraic expressions with the expansion coefficients of the U(4)⊃SUS(2)⊗SUT(2) states in terms of those in the U(4) canonical basis and the Clebsch-Gordan coefficients of U(4) in the canonical basis. The state expansion coefficients are evaluated as the components of the null space vectors of the spin-isospin projection matrices. Program summaryProgram Title: Wigner-U4-SU2xSU2CPC Library link to program files:https://doi.org/10.17632/4b7gf2phh2.1Licensing provisions: GPLv3Programming language: Wolfram Mathematica version 9.0.1.0 and beyondNature of problem: Numerical evaluation of the elementary Wigner coefficients (EWCs) of U(4)⊃SUS(2)⊗SUT(2).Solution method: Mathematica implementation of the EWCs of U(4)⊃SUS(2)⊗SUT(2) [1] using the expansion coefficients of U(4)⊃SUS(2)⊗SUT(2) states in terms of those of the U(4) canonical basis determined as components of the null space vectors of the spin-isospin projection matrices [2].

Nucleon-nucleon scattering parameters in the limit of SU(3) flavor symmetry

The scattering lengths and effective ranges that describe low-energy nucleon-nucleon scattering are calculated in the limit of SU(3)-flavor symmetry at the physical strange-quark mass with Lattice Quantum Chromodynamics. The calculations are performed with an isotropic clover discretization of the quark action in three volumes with spatial extents of L \sim 3.4 fm, 4.5fm and 6.7 fm, and with a lattice spacing of b \sim 0.145 fm. With determinations of the energies of the two-nucleon systems (both of which contain bound states at these up and down quark masses) at rest and moving in the lattice volume, Luscher's method is used to determine the low-energy phase shifts in each channel, from which the scattering length and effective range are obtained. The scattering parameters, in the 1S0 channel are found to be m_pi a^(1S0) = 9.50^{+0.78}_{-0.69}^{+1.10}_{-0.80} and m_pi r^(1S0) = {4.61^{+0.29}_{-0.31}^{+0.24}_{-0.26}, and in the 3S1 channel are m_pi a^(3S1) = 7.45^{+0.57}_{-0.53}^{+0.71}_{-0.49} and m_pi r^(3S1) = 3.71^{+0.28}_{-0.31}^{+0.28}_{-0.35}. These values are consistent with the two-nucleon system exhibiting Wigner's supermultiplet symmetry, which becomes exact in the limit of large-N_c. In both spin channels, the phase shifts change sign at higher momentum, near the start of the t-channel cut, indicating that the nuclear interactions have a repulsive core even at the SU(3)-symmetric point.

The emergence of symmetries in complex nuclei

After a brief review of early developments, two recent examples of applications of symmetries in nuclear physics are presented: (i) pseudo-spin symmetry which can be used to extend Wigner's supermultiplet model to heavy nuclei; (ii) symmetries of the interacting boson model with isoscalar and isovector bosons which can be used to analyze the problem of deuteron transfer in N = Z nuclei.

Nucleon-nucleon potential in the 1/Nc expansion

The nucleon-nucleon potential is analyzed using the 1/N{sub c} expansion of QCD. The NN potential is shown to have an expansion in 1/N{sub c}{sup 2}, and the strengths of the leading order central, spin-orbit, tensor, and quadratic spin-orbit forces (including isospin dependence) are determined. Comparison with a successful phenomenological potential (Nijmegen) shows that the large-N{sub c} analysis explains many of the qualitative features observed in the nucleon-nucleon interaction. The 1/N{sub c} expansion implies an effective Wigner supermultiplet symmetry for light nuclei. Results for baryons containing strange quarks are presented in an appendix. {copyright} {ital 1997} {ital The American Physical Society}

Scissors Modes and Spin Excitations in Light Nuclei IncludingΔN=2 Excitations: Behaviour of8Be and10Be

Shell model calculations are performed for magnetic dipole excitations in8Be and10Be, first with a quadrupole–quadrupole interaction (Q·Q) and then with a realistic interaction. The calculations are performed both in a 0pspace and in a large space which includes all 2ℏωexcitations. In the 0pwithQ·Qwe have an analytic expression for the energies of all states. In this limit we find that in10Be theL=1S=0 scissors mode with isospinT=1 is degenerate with that ofT=2. By projection from an intrinsic state we can obtain simple expressions forB(M1) to the scissors modes in8Be and10Be. We plot cumulative sums for energy-weighted isovector orbital transitions fromJ=0+ground states to the 1+excited states. These have the structure of a low-energy plateau and a steep rise to a high-energy plateau. The relative magnitudes of these plateaux are discussed. By comparing8Be and10Be we find that contrary to the behaviour in heavy deformed nuclei,B(M1)orbitalis not proportional toB(E2). On the other hand, a sum rule which relatesB(M1) to the difference (B(E2)isoscalar−B(E2)isovector) succeeds in describing the difference in behaviours in the two nuclei. The results forQ·Qand the realistic interactions are compared, as are the results in the 0pspace and the large (0p+2ℏω) space. The Wigner supermultiplet scheme is a very useful guide in analyzing the shell model results.

The spin-flavor dependence of nuclear forces from large- N QCD

We show that nuclear interactions are SU(4) symmetric at leading order in chiral perturbation theory in the large- N limit of QCD. The nucleons and delta resonances form a 20-dimensional representation of SU(4) and we show how Wigner's supermultiplet symmetry SU(4) sm, under which the nucleons transform as a 4-dimensional representation, follows as an accidental low energy symmetry. Exploiting SU(4) symmetry allows one to express the 18 independent leading N, Δ interaction operators invariant under SU(2) I × SU(2) J in terms of only two couplings. The three flavor analogue allows one to express the 28 leading octet, decuplet interactions in terms of only two couplings, which has implications for hypernuclei and strangeness in “neutron” stars.

Isospin invariant boson models for fp-shell nuclei

Isospin invariant boson models, IBM-3 and IBM-4, applicable in nuclei with neutrons and protons in the same valence shell, are reviewed. Some basic results related to these models are discussed: the mapping onto the shell model, the relation to Wigner's supermultiplet scheme, the boson-number and isospin dependence of parameters, etc. These results are examined for simple single-j shell situations (e.g. f7/2) and their extension to the fp shell is investigated. Other extensions discussed here concern the treatment of odd-mass nuclei and the classification of particle-hole excitations in light nuclei. The possibility of a pseudo-SU(4) supermultiplet scheme in fp-shell nuclei is discussed.

A double rotor coherent state construction of the Wigner supermultiplet SU(4) contains/implies SU(2)*SU(2)

A double rotor vector coherent state construction of the SU(4) 3 SU(2) x Sup) Wigner supermultiplet leads to a simple matrix representation of this scheme. Matrix elements of the vector coherent state realizations of the group generators are given by very simple expressions in tem of ordinary spin (S) and isospin (T) Wigner coefficients with intrinsic projection labels KS and Kg. The K-mawix technique is used to effectively elevate these labels lo the status of good quantum numbers. The KKt matrices Bre given in analytic form for a number of impomt irreducible representations.

Symmetry in the Nucleon-Nucleon Interaction and the Model of Moscow Potential

An attempt to understand better the modern situation with short range baryon-baryon (by example of nucleon-nucleon) interaction is undertaken. The article covers five main ingredients of the whole problem: (i) visual demonstration of the inadequacy of modern models for short-range N − N interaction, (ii) the general property of the Wigner supermultiplet symmetry of interaction potentials for composite particles, (iii) a short outline of the main results of realistic six-quark microscopic calculations for nucleon-nucleon interaction and the results based on the Moscow model for N − N interaction, (iv) supersymmetry between the Moscow and conventional models for the N − N interaction and (v) some general implications for nuclear physics at whole. In particular, on the basis of the picture we suggest and substantiate microscopically the formation of specific nuclear bonds rather similar to the quantum chemistry case. In this pattern, e.g., the structure of the 4He-nucleus is similar to the structure of the CH4-methane molecule having tetrahedral form due to the formation of the π-electron bonds, each consisted of a pair of p-electrons with the opposite spin directions. It is also shown that the Moscow model of N − N interaction is an alone model comprising a wide repulsive core of ∼1 fm size dictated by modern electron data for the lightest nuclei 3He and 4He. Some arguments are given showing that the moel considered can lead to solving of many long standing puzzles in nuclear physics, in particular to avoiding the nucleus collapse predicted many years ago when using realistic (e.g., RHC) N − N force and ensure the saturation property of nuclear forces.

Symmetry in the Nucleon-Nucleon Interaction and the Model of Moscow Potential

An attempt to understand better the modern situation with short range baryon-baryon (by example of nucleon-nucleon) interaction is undertaken. The article covers five main ingredients of the whole problem: (i) visual demonstration of the inadequacy of modern models for short-range N-N interaction, (ii) the general property of the Wigner supermultiplet symmetry of interaction potentials for composite particles, (iii) a short outline of the main results of realistic six-quark microscopic calculations for nucleon-nucleon interaction and the results based on the Moscow model for N-N interaction

Effect of ground-state correlation on the total Gamow-Teller strength of doubly LS closed shell nuclei

The total Gamow-Teller (GT) strength in the doubly LS closed-shell nuclei is calculated by the sum-rule technique in the shell model. 2p2h states are admixed to the ground state in first-order perturbation. The deviation of the orbital occupancy from that of the closed shell state is found to produce a considerable amount of GT strength. It is shown, however, that the total GT strength produced gets reduced by about one-half by the proton-neutron correlation effect. From the point of view of the Wigner supermultiplet SU(4) theory, the proton-neutron correlation effect and the tensor-force dominant property of the total GT strength are successfully explained.

Fermion dynamical symmetry model of 2s-1d shell

In the framework of shell model, we discussed the fermion dynamical symmetries in 2s-1d shell. Assuming the L-S coupling and the Wigner supermultiplet, we get a U(24) fermion dynamical symmetry. All possible subgroup chains are discussed. We have found that 32S seems to exhibit U(5) dynamical symmetry.

Canonical orthonormal Wigner supermultiplet basis

The explicit construction of an orthonormal basis for states of good spin, isospin and SU(4) Wigner supermultiplet symmetry is given in a Bargmann representation space. A complete set of quantum labels is provided by a Sp(3, R) contains/implies U(3) complementary symmetry.

M1 strengths and sum rules in the Wigner supermultiplet scheme

The non-energy-weighted (NEW) sum-rule strength for the M1 operator and the B(M1) strengths in the ground-state region are evaluated in the SU(4) basis. Here, one combines the spectral distribution method of calculating the intensities of the different irreducible representations with the method of evaluation of M1 strengths between two SU(4) ST states through SU(4) algebra. Comparison with experimental and shell-model values in the lower half of the ds shell is made.

Supermultiplet symmetry in nuclear reactions: Application toHe3(p, H2)2pandBe9(H3,He6)Li6

A detailed analysis of the extension of the Barshay-Temmer theorem to reaction product pairs that are members of the same SU(4) multiplet (Wigner supermultiplet) is presented. Nonzero values of the total orbital angular momentum within fragments in the presence of residual spin orbit splitting is shown to destroy symmetry of the reaction products around 90\ifmmode^\circ\else\textdegree\fi{} except in a sum rule sense. Departures from reaction symmetry are related to the SU(4) breaking parameter in the effective nucleon-nucleon potential and it is shown that the asymmetry should decrease with increasing $A$. A comparison of the $^{3}\mathrm{He}(p, ^{2}\mathrm{H})2p$ and $^{9}\mathrm{Be}$($^{3}\mathrm{H}$, $^{6}\mathrm{He}$)$^{6}\mathrm{Li}$ angular distributions illustrates this point. Finally, a prediction is made for the ratio of analyzing powers for the $^{6}\mathrm{He}$+$^{6}\mathrm{Li}$ and $^{6}\mathrm{He}$+$^{6}\mathrm{Li}$*(3.56) final states.NUCLEAR REACTIONS Antisymmetric scattering theory. Symmetry around 90\ifmmode^\circ\else\textdegree\fi{} of $\ensuremath{\sigma}(\ensuremath{\theta})$ for $a(b, c){c}^{\ensuremath{'}}$ reactions derived for SU(4) invariant potentials. Angular symmetry breakdown related to size of SU(4) breaking potential through DWBA. Discussion of $^{3}\mathrm{He}(p, d)2p$, $^{9}\mathrm{Be}(t, ^{6}\mathrm{He})^{6}\mathrm{Li}(^{6}\mathrm{Li}^{*})$, and $^{9}\mathrm{Be}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{t}}, ^{6}\mathrm{He})^{6}\mathrm{Li}(^{6}\mathrm{Li}^{*})$ reactions.

An intrinsic spin for interacting bosons

The addition, to the usual set of T=1 bosons, of s and d bosons with T=0 and an intrinsic spin of S=1 leads to a version of the IBM which incorporates the Wigner supermultiplet symmetry.

What Does the Franzini-Radicati Mass Relationship Imply about the Wigner Supermultiplet Symmetry?

The Franzini-Radicati mass relationship between isobars is reexamined to find out whether it provides a good test of the Wigner SU(4) symmetry in nuclei. It is found that the mass ratio is an extremely insensitive function of the symmetry mixing.

Spectral distributions and the breaking of isospin and supermultiplet symmetries in nuclei

Knowledge of the Racah algebra for the higher unitary groups is exploited to give a general formula for the partial widths for the direct product subgroup U( N k )× U(k) of the full unitary group U( N) of a given shell model vector space. This formula makes it possible to separate the second moments of dynamical operators into the internal and external parts which are needed for detailed applications of the spectral distribution technique. Specific applications are made for k = 2 (isospin) and k = 4 (Wigner supermultiplet symmetry). Explicit expressions are given for the isospin breaking contributions to the spectral widths which make it possible to estimate the intensities of isospin impurities in an average state of a given isospin. The goodness of Wigner supermultiplet symmetry is examined for the 2s-ld shell with a detailed example, the A = 25 nuclei, for which partial widths have been calculated for various modifications of the Kuo-Brown interaction to give a simple measure of the amount of mixing to be expected between states of different space symmetry.

Space symmetry in light nuclei: (II). SU(4) isospin-spin averages

The validity of the Wigner supermultiplet scheme in the d-s shell is investigated for nuclei with neutron excess using the spectral distribution methods of French. Averages of the Hamiltonian H and H 2 over states belonging to a definite SU(4) symmetry, isospin and spin are used to determine ground state energies and low lying spectra of nuclei. Intensities of various irreducible representations of SU(4) near the ground state are evaluated and these provide a measure of symmetry breaking. We find that the symmetry in nuclei with neutron excess is no worse than that for the lowest isospin ones. The results obtained are compared with the Franzini-Radicati mass formula.

Space symmetry in light nuclei. I Application to the 2 s−1 d shell

The Wigner supermultiplet scheme is studied in the 2 s−1 d shell using the spectral distribution methods of French. Expressions for the average expectation value of H and H 2 over states belonging to a definite SU(4) symmetry are derived. Numerical results for these averages are given for the 2 s−1 d shell. These averages are then used to predict ground state energies and low energy spectra for nuclei in this shell, using Ratcliff's procedure; a comparison with shell model and observed spectra is made. Mixing intensities of SU(4) representations near the ground state are also evaluated. These provide us with a measure of symmetry breaking. It appears from our calculations that the symmetry is strongly mixed. Finally a preliminary application to the theory of level densities is made.