Evidence for the Existence of Supersymmetry in Atomic Nuclei

Metz, A.; Jolie, J.; Graw, G.; Hertenberger, R.; Gröger, J.; Günther, C.; Warr, N.; Eisermann, Y.

doi:10.1103/physrevlett.83.1542

Cited by 107 publications

(75 citation statements)

References 17 publications

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“…On the other hand, in nuclear physics supersymmetry was predicted theoretically [2] and has been confirmed experimentally [3] as a dynamic symmetry linking properties of some bosonic and fermionic nuclei. It would be interesting to look for some physical systems whose special properties could be explained by a hidden ordinary (not a dynamic) supersymmetry.…”

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confidence: 88%

Hidden nonlinear supersymmetry of finite-gap Lamé equation

2007

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A bosonized nonlinear (polynomial) supersymmetry is revealed as a hidden symmetry of the finite-gap Lamé equation. This gives a natural explanation for peculiar properties of the periodic quantum system underlying diverse models and mechanisms in field theory, nonlinear wave physics, cosmology and condensed matter physics. PACS numbers: 11.30.Pb; 11.30.Na; 03.65.Fd Supersymmetry [1], as a fundamental symmetry providing a natural mechanism for unification of gravity with electromagnetic, strong and weak interactions, still waits for experimental confirmation. On the other hand, in nuclear physics supersymmetry was predicted theoretically [2] and has been confirmed experimentally [3] as a dynamic symmetry linking properties of some bosonic and fermionic nuclei. It would be interesting to look for some physical systems whose special properties could be explained by a hidden ordinary (not a dynamic) supersymmetry.In the present Letter we show that the quantum system described by the finite-gap Lamé equation possesses a hidden supersymmetry. A very unusual nature of the revealed supersymmetry is that it manifests as a nonlinear symmetry of a bosonic system without fermion (spin) degrees of freedom. This means that we find here a kind of a bosonized supersymmetry giving a natural explanation for peculiar properties of the periodic quantum problem underlying many physical systems.The Lamé equation first arose in solution of the Laplace equation by separation of variables in ellipsoidal coordinates [4], and one of its early applications was in the quantum Euler top problem [5]. It plays nowadays a prominent role in physics appearing in such diverse theories as crystals models in solid state physics [6,7], exactly and quasi-exactly solvable quantum systems [8,9], integrable systems and solitons [10,11] [21], and preheating after inflation modern theories [22]. Most often, the Lamé equation appears in physics literature in the Jacobian form of a one-dimensional Schrodinger equation with a doubly periodic potential,where sn(x, k) ≡ sn x is the Jacobi elliptic odd function with modulus k (0 < k < 1), and real and imaginary periods 4K and 2iK ′ , K = K(k) is a complete elliptic integral of the first kind, and 4,23]. A remarkable property of this equation is that at integer values of the parameter j = n, its energy spectrum has exactly n gaps, which separate the n+1 allowed energy bands. The 2n + 1 eigenfunctions associated to the boundaries E i (n), i = 0, 1, . . . , 2n, of the allowed energy bands, ∞] are given by polynomials ('Lamé polynomials') of degree n in the elliptic functions sn x, cn x and dn x. These polynomials have real periods 4K or 2K, and the boundary energy levels E i (n) are non-degenerated. The states in the interior of allowed zones are described by the quasi-periodic Bloch-Floquet wave functions (which can be expressed in terms of theta functions [4]) of quasi-momentum κ(E),Every such interior energy level is doubly degenerated. For any non-integer value of the parameter j, Eq. (1) has an infinite num...

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confidence: 88%

Hidden nonlinear supersymmetry of finite-gap Lamé equation

2007

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“…The choice of the parameters in the Hamiltonian is not important for the calculation of spectroscopic strengths since the eigenstates are given by the quantum numbers labeling the irreducible representations (irreps) of the chain of groups chosen, and they are the same for any choice of parameters. For this reason, any set of parameters given in the literature [7,9] for the description of these nuclei will be good for our calculations. Although the energies will be different for each set, the structure of the wave functions is given by the n-SUSY scheme.…”

Section: Pt → 195 Pt Described With N-susymentioning

confidence: 99%

“…During this time the theoretical and experimental effort for identifying some nuclei as examples of the realization of n-SUSY was mainly concentrated in the comparison of the predicted and observed level schemes. Recently, however, new experimental facilities have allowed detailed measurements of nuclear properties in the Pt region [7][8][9][10], particularly one nucleon transfer intensities. These experimental data have allowed more stringent testing of the idea of n-SUSY and have provided strong evidence of its existence in nature.…”

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confidence: 99%

One nucleon transfer operator and nuclear supersymmetry

et al. 2005

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The appropriate use of the interacting boson-fermion model one nucleon transfer operator in connection with nuclear supersymmetries is discussed. We emphasize that care must be taken in using the same coupling order, either l-s or s-l, in the odd particle creation operator appearing in the one nucleon transfer operator and in the wave function of the odd-A nucleus. As an example, we have recalculated consistently the one nucleon transfer strengths for the 196 Pt → 195 Pt one neutron pickup reaction which is the best known example of dynamical nuclear supersymmetry. In addition, we present for the same reaction the results of several calculations considering different truncations in the boson-fermion expansion of the fermion creation operator.

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“…Introduction -Supersymmetry as a fundamental symmetry of Nature still waits for experimental confirmation, but as a kind of symmetry between bosonic and fermionic states, it already turned out to be fruitful in diverse areas, including nuclear [1,2], atomic, solid-state, and statistical physics [3]. Supersymmetric quantum mechanics [3] was introduced under investigation of the problem of supersymmetry breaking in field theory [4].…”

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Self-Isospectrality, Special Supersymmetry, and their Effect on the Band Structure

et al. 2008

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We study a planar model of a non-relativistic electron in periodic magnetic and electric fields that produce a 1D crystal for two spin components separated by a half-period spacing. We fit the fields to create a self-isospectral pair of finite-gap associated Lamé equations shifted for a half-period, and show that the system obtained is characterized by a new type of supersymmetry. It is a special nonlinear supersymmetry generated by three commuting integrals of motion, related to the parityodd operator of the associated Lax pair, that coherently reflects the band structure and all its peculiarities. In the infinite period limit it provides an unusual picture of supersymmetry breaking.

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Evidence for the Existence of Supersymmetry in Atomic Nuclei

Cited by 107 publications

References 17 publications

Hidden nonlinear supersymmetry of finite-gap Lamé equation

Hidden nonlinear supersymmetry of finite-gap Lamé equation

One nucleon transfer operator and nuclear supersymmetry

Self-Isospectrality, Special Supersymmetry, and their Effect on the Band Structure

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