234 research outputs found

    A new effective interaction for the trapped Fermi gas

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    We apply the configuration-interaction method to calculate the spectra of two-component Fermi systems in a harmonic trap, studying the convergence of the method at the unitary interaction limit. We find that for a fixed regularization of the two-body interaction the convergence is exponential or better in the truncation parameter of the many-body space. However, the conventional regularization is found to have poor convergence in the regularization parameter, with an error that scales as a low negative power of this parameter. We propose a new regularization of the two-body interaction that produces exponential convergence for systems of three and four particles. From the systematics, we estimate the ground-state energy of the four-particle system to be (5.05 +- 0.024)hbar omega.Comment: 4 pages, 3 figure

    Fermionic Symmetries: Extension of the two to one Relationship Between the Spectra of Even-Even and Neighbouring Odd mass Nuclei

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    In the single j shell there is a two to one relationship between the spectra of certain even-even and neighbouring odd mass nuclei e.g. the calculated energy levels of J=0^+ states in ^{44}Ti are at twice the energies of corresponding levels in ^{43}Ti(^{43}Sc) with J=j=7/2. Here an approximate extension of the relationship is made by adopting a truncated seniority scheme i.e. for ^{46}Ti and ^{45}Sc we get the relationship if we do not allow the seniority v=4 states to mix with the v=0 and v=2 states. Better than that, we get very close to the two to one relationship if seniority v=4 states are admixed perturbatively. In addition, it is shown that the higher isospin states do not contain seniority 4 admixtures.Comment: 11 pages, RevTex file and no figures, typos added, references changed and changed content

    Isoscalar g Factors of Even-Even and Odd-Odd Nuclei

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    We consider T=0 states in even-even and odd-odd N=Z nuclei. The g factors that emerge are isoscalar. We find that the single j shell model gives simple expressions for these g factors which for even-even nuclei are suprisingly close to the collective values for K=0 bands. The g factors of many 2+ in even-even nuclei and 1+ and 3+ states in odd-odd nuclei have g factors close to 0.5

    JJ-pairing interaction, number of states, and nine-jj sum rules of four identical particles

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    In this paper we study JJ-pairing Hamiltonian and find that the sum of eigenvalues of spin II states equals sum of norm matrix elements within the pair basis for four identical particles such as four fermions in a single-jj shell or four bosons with spin ll. We relate number of states to sum rules of nine-jj coefficients. We obtained sum rules for nine-jj coefficients and and summing over (1) even JJ and KK, (2) even JJ and odd KK, (3) odd JJ and odd KK, and (4) both even and odd J,KJ,K, where jj is a half integer and ll is an integer.Comment: 6 pages, no figure, updated version, to be published. Physical Review C, in pres

    A new effective interaction for the trapped fermi gas: the BEC-BCS crossover

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    We extend a recently introduced separable interaction for the unitary trapped Fermi gas to all values of the scattering length. We derive closed expressions for the interaction matrix elements and the two-particle eigenvectors and analytically demonstrate the convergence of this interaction to the zero-range two-body pseudopotential for s-wave scattering. We apply this effective interaction to the three- and four-particle systems along the BEC-BCS crossover, and find that their low-lying energies exhibit convergence in the regularization parameter that is much faster than for the conventional renormalized contact interaction. We find similar convergence properties of the three-particle free energy at unitarity.Comment: 10 pages, 7 figure

    Pairing of Parafermions of Order 2: Seniority Model

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    As generalizations of the fermion seniority model, four multi-mode Hamiltonians are considered to investigate some of the consequences of the pairing of parafermions of order two. 2-particle and 4-particle states are explicitly constructed for H_A = - G A^+ A with A^+}= 1/2 Sum c_{m}^+ c_{-m}^+ and the distinct H_C = - G C^+ C with C^+}= 1/2 Sum c_{-m}^+ c_{m}^+, and for the time-reversal invariant H_(-)= -G (A^+ - C^+)(A-C) and H_(+) = -G (A^+dagger + C^+)(A+C), which has no analogue in the fermion case. The spectra and degeneracies are compared with those of the usual fermion seniority model.Comment: 18 pages, no figures, no macro

    Classification of states of single-jj fermions with JJ-pairing interaction

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    In this paper we show that a system of three fermions is exactly solvable for the case of a single-jj in the presence of an angular momentum-JJ pairing interaction. On the basis of the solutions for this system, we obtain new sum rules for six-jj symbols. It is also found that the "non-integer" eigenvalues of three fermions with angular momentum II around the maximum appear as "non-integer" eigenvalues of four fermions when II is around (or larger than) JmaxJ_{\rm max} and the Hamiltonian contains only an interaction between pairs of fermions coupled to spin J=Jmax=2j−1J=J_{\rm max}=2j-1. This pattern is also found in five and six fermion systems. A boson system with spin ll exhibits a similar pattern.Comment: to be published in Physical Review

    General pairing interactions and pair truncation approximations for fermions in a single-j shell

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    We investigate Hamiltonians with attractive interactions between pairs of fermions coupled to angular momentum J. We show that pairs with spin J are reasonable building blocks for the low-lying states. For systems with only a J = Jmax pairing interaction, eigenvalues are found to be approximately integers for a large array of states, in particular for those with total angular momenta I le 2j. For I=0 eigenstates of four fermions in a single-j shell we show that there is only one non-zero eigenvalue. We address these observations using the nucleon pair approximation of the shell model and relate our results with a number of currently interesting problems.Comment: a latex text file and 2 figures, to be publishe

    Generalized seniority scheme in light Sn isotopes

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    The yrast generalized seniority states are compared with the corresponding shell model states for the case of the Sn isotopes 104−112^{104-112}Sn. For most of the cases the energies agree within 100 keV and the overlaps of the wave functions are greater than 0.7.Comment: 8 pages, revtex. Submitted to Phys. Rev.
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