Exact evaluation of the nuclear form factor for new kinds of majoron emission in neutrinoless double beta decay

doi:10.1016/S0370-2693(96)01587-0

Physics Letters B

Volume 392, Issues 3–4, 30 January 1997, Pages 419-425

https://doi.org/10.1016/S0370-2693(96)01587-0 Get rights and content

Abstract

We have developed a formalism, based on the Fourier-Bessel expansion, that facilitates the evaluation of matrix elements involving nucleon recoil operators, such as appear in several exotic forms of neutrinoless double beta decay (ββ_0ν). The method is illustrated by applying it to the “charged” majoron model, which is one of the few that can hope to produce an observable effect. From our numerical computations within the QRPA performed for ⁷⁶Ge, ⁸²Se, ¹⁰⁰Mo, ¹²⁸Te and ¹⁵⁰Nd nuclei, we test the validity of approximations made in earlier work to simplify the new matrix elements, showing that they are accurate to within 15%. Our new method is also suitable for computing other previously unevaluated ββ_0ν nuclear matrix elements.

References (24)

G.B. Gelmini et al.
Phys. Lett. B
(1981)
M.C. Gonzalez-Garcia et al.
Phys. Lett. B
(1989)
C.P. Burgess et al.
Phys. Lett. B
(1993)
C.P. Burgess et al.
Phys. Rev. D
(1994)
P. Bamert et al.
Nucl. Phys. B
(1995)
C. Barbero et al.
Phys. Lett. B
(1996)
M. Hirsch et al.
Phys. Lett. B
(1996)
F. Krmpotić et al.
Nucl. Phys. A
(1992)
M. Doi et al.
Phys. Rev. D
(1988)
M. Doi et al.
Prog. Theor. Phys. Suppl.
(1985)
T. Tomoda et al.
Nucl. Phys. A
(1986)

T. Tomoda

Rep. Prog. Phys.

(1991)

G.S. Abrams

Phys. Rev. Lett.

(1989)

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Limits on different majoron decay modes of 100Mo and 82Se for neutrinoless double beta decays in the NEMO-3 experiment
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The NEMO-3 tracking detector is located in the Fréjus Underground Laboratory. It was designed to study double beta decay in a number of different isotopes. Presented here are the experimental half-life limits on the double beta decay process for the isotopes ¹⁰⁰Mo and ⁸²Se for different majoron emission modes and limits on the effective neutrino–majoron coupling constants. In particular, new limits on “ordinary” majoron (spectral index 1) decay of ¹⁰⁰Mo ( $T_{1 / 2} > 2.7 \times 10^{22} yr$ ) and ⁸²Se ( $T_{1 / 2} > 1.5 \times 10^{22} yr$ ) have been obtained. Corresponding bounds on the majoron–neutrino coupling constant are $〈 g_{e e} 〉 < (0.4 – 1.8) \times 10^{−4}$ and $< (0.66 – 1.9) \times 10^{−4}$ .
Double beta decay of σ- hyperons
2003, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
We compute the strangeness-conserving double beta decay of Σ⁻ hyperons, which is the only hadronic system that can undergo such decays. We consider both, the lepton number conserving $Σ^{−} → Σ^{+} e^{−} e^{−} ν ̄ ν ̄$ (ββ_{Σ_2ν}) and the lepton number violating Σ⁻→Σ⁺e⁻e⁻ (ββ_{Σ_0ν}) modes. The branching ratios of these ββ decays are suppressed at the level of 10⁻³⁰ considering a light neutrino scenario in the case of the ββ_{Σ_0ν} channel. The dynamical origin of such low rates and their possible enhancements are briefly discussed. Given its simplicity those decays can be used also for the purposes of illustrating the main features of double beta decays.
Nuclear data sheets for A = 82
2003, Nuclear Data Sheets
The 1995 evaluation of A=82 (1987Mu01) has been revised using experimental decay and reaction data received by the cutoff date noted below. Major developments are:
⁸²Ni: A few theoretical references calculating pairing correlation energies, but nuclide not seen.
⁸²Zn: Produced in fission. No properties known.
⁸²Ge: Some pairing calculations.
⁸²As: 1− isomer adopted as g.s.; 5− excitation energy is uncertain.
⁸²Rb: New (HI,xnγ) data.
⁸²Se: Large number of measurements on 0v and 2v 2β⁻ decay. Major new work is (n,n′γ).
⁸²Y: New T_1/2. New (HI,xnγ) data.
⁸²Zr: New (HI,xnγ); many new bands.
⁸²Nb: Measured half-life, inferred β⁺ decay.
⁸²Mo: Calculated mass, etc, nuclide not observed.
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1999, Nuclear Physics A
The recently developed formalism for the evaluation of nuclear form factors in neutrinoless double beta decay is applied to ⁴⁸Ca, ⁷⁶Ge, ⁸²Se, ¹⁰⁰Mo, ¹²⁸Te and ¹³⁰Te nuclei. Explicit analytical expressions that follows from this theoretical development, in the single-mode model for the decay of ⁴⁸Ca, have been worked out. They are useful both for testing the full numerical calculations, and for analytically checking the consistency with other formalisms. Large configuration space calculations are compared with previous studies, where alternative formulations were used. Yet, besides using the G-matrix as residual interaction, we here use a simple δ-force. Attention is paid to the connected effects of the short range nuclear correlations and the finite nucleon size. Constraints on lepton number violating terms in the weak Hamiltonian (effective neutrino Majorana mass and effective right-handed current coupling strengths) are deduced.
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^☆: Work partially supported by the Fundación Antorchas, Argentina, the CONICET from Argentina, the Universidad Nacional de La Plata, NSERC of Canada and FCAR of Québec.

¹: Fellow of the CONICET from Argentina.

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Physics Letters B

Abstract

References (24)

Phys. Lett. B

Phys. Lett. B

Phys. Lett. B

Phys. Rev. D

Nucl. Phys. B

Phys. Lett. B

Phys. Lett. B

Nucl. Phys. A

Phys. Rev. D

Prog. Theor. Phys. Suppl.

Nucl. Phys. A

Rep. Prog. Phys.

Phys. Rev. Lett.

Cited by (15)

Limits on different majoron decay modes of <sup>100</sup>Mo and <sup>82</sup>Se for neutrinoless double beta decays in the NEMO-3 experiment

Double beta decay of σ<sup>-</sup> hyperons

Nuclear data sheets for A = 82

Nuclear moments for the neutrinoless double beta decay II

Weak magnetism in two neutrino double beta decay

Competition between standard and exotic double beta decays

Exact evaluation of the nuclear form factor for new kinds of majoron emission in neutrinoless double beta decay☆

Abstract

Phys. Lett. B

Phys. Lett. B

Phys. Lett. B

Phys. Rev. D

Nucl. Phys. B

Phys. Lett. B

Phys. Lett. B

Nucl. Phys. A

Phys. Rev. D

Prog. Theor. Phys. Suppl.

Nucl. Phys. A

Rep. Prog. Phys.

Phys. Rev. Lett.