Influence of pairing and deformation on charge exchange transitions

Authors

  • A. Carranza M. Instituto de Ciencias Nucleares, UNAM http://orcid.org/0000-0002-2170-9903
  • S. Pittel Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA.
  • Jorge G. Hirsch Instituto de Ciencias Nucleares, UNAM

DOI:

https://doi.org/10.31349/RevMexFis.66.710

Keywords:

Charge-exchange reactions, Gamow-Teller, pairing, deformation

Abstract

We describe the importance of charge-exchange reactions, and in particular Gamow-Teller transitions, first to astrophysical processes and double beta decay, and then to the understanding of nuclear structure. In our review of their role in nuclear structure we first provide an overview of some of the key steps in the emergence of our current understanding of the structure of nuclei, including the central role played by the isovector pairing and the quadrupole-quadrupole channels in the description of energy spectra and in the manifestation of collective modes, some associated with deformation of the nuclear shape. We then turned our focus to Gamow-Teller (GT) tran- sitions in relatively light nuclei, especially in the 2p1f shell, where isoscalar pairing may be playing a role in competition with the isovector pairing that dominates in heavier regions. Following a summary of the progress made in recent years on this subject, we report a systematic shell model study aimed at providing further clarification as to how these pairing modes compete. In this study, we use a schematic Hamiltonian that contains a quadrupole- quadrupole interaction as well as both isoscalar and isovector pairing interac- tions. We first find an optimal set of Hamiltonian parameters for the model, to provide a starting point from which to vary the relevant pairing strengths and thus assess how this impacts the behavior of GT transitions and the corresponding energy spectra and rotational properties of the various nuclei involved in the decays. The analysis includes as an important theme a com- parison with experimental data. The need to suppress the isoscalar pairing mode when treating nuclei with a neutron excess to avoid producing spurious results for the ground state spin and parity with the simplified Hamiltonian is highlighted. Varying the strength parameters for the two pairing modes is found to exhibit different but systematic effects on GT transition properties and on the corresponding energy spectra, which are detailed.

References

Missing and quenched Gamow-Teller strength, E. Caurier, A. Poves, A.P. Zuker, Phys. Rev. Lett. 74 (1995) 1517- 1520.

Gamow-Teller strengths and electron-capture rates for pf- shell nuclei of relevance for late stellar evolution, A. L. Cole, T. S. Anderson, R. G. T. Zegers, Sam M. Austin, B. A. Brown, L. Valdez, S. Gupta, G. W. Hitt, and O. Fawwaz, Phys. Rev. C 86 (2012) 015809.

Shell model description of Gamow-Teller strengths in pf- shell nuclei, Vikas Kumar and P.C. Srivastava, Eur. Phys. J. A 52 (2016) 181.

Nuclear beta-decay half-lives for fp and fpg shell nuclei, Vikas Kumar, P C Srivastava and Hantao Li, J. Phys. G: Nucl. Part. Phys. 43 (2016) 105104.

Nuclear weak-interaction processes in stars, K. Langanke and G. Mart ́ınez-Pinedo, Rev. Mod. Phys. 75 (2003) 819.

Neutrino-nucleus reactions and their role for supernova dy- namics and nucleosynthesis, K.G. Balasi, K. Langanke, G. Mart ́ınez-Pinedo, Prog. Part. Nucl. Phys. 85 (2015) 33-81.

Two-Neutrino Double-Beta Decay, Ruben Saakyan, Annu. Rev. Nucl. Part. Sci. 63 (2013) 503-529.

Neutrinoless Double-Beta Decay: Status and Prospects, Michelle J. Dolinski, Alan W.P. Poon, and Werner Rode- johann, Annu. Rev. Nucl. Part. Sci. 69 (2019) 219-251.

Neutrino Nucleosynthesis, A. Heger, E. Kolbe, W. C. Hax- ton, K. Langanke, G. Mart ́ınez-Pinedo, and S. E.Woosley, Phys. Lett. B 606 (2005) 258.

Element synthesis in the supernova environment and neu- trino oscillations, T. Suzuki and T. Kajino, J. Phys. G 40 (2013) 083101.

Gamow-Teller Strength in the Exotic Odd-Odd Nuclei 138La and 180Ta and Its Relevance for Neutrino Nucleosyn- thesis, A. Byelikov, T. Adachi, H. Fujita, K. Fujita, Y. Fu- jita, K. Hatanaka, A. Heger, Y. Kalmykov, K. Kawase, K. Langanke et al., Phys. Rev. Lett. 98 (2007) 082501.

Hartree-Fock-Bogoliubov Theory with Applications to Nu- clei, A.L. Goodman, in : Advances in Nuclear Physics, Vol. 11, eds. J.W. Negele and E. Vogt (Plenum, New York, 1979) 263.

For a concise historical revision with references see J. Dobaczewski (2004), https://www.fuw.edu.pl/ dobaczew/nppair60w/node2.html.

Systematic study of proton-neutron pairing correlations in the nuclear shell model, Y. Lei, S. Pittel, N. Sandulescu, A. Poves, B. Thakur and Y. M. Zhao, Phys. Rev. C 84 (2011) 044318.

Breaking of the SU(4) limit for the Gamow-Teller strength in N Z nuclei, I. Petermann, G. Martinez-Pinedo, K. Langanke, and E. Caurier, Eur. Phys. J. A 34 (2007) 319- 324.

Exact Solution of the Spin-Isospin Proton-Neutron Pairing Hamiltonian, S. Lerma H., B. Errea, J. Dukelsky, and W. Satula, Phys. Rev. Lett. 99 (2007) 032501.

Isovector neutron-proton pairing with particle number pro- jected BCS, N. Sandulescu, B. Errea, and J. Dukelsky, Phys. Rev. C 80 (2009) 044335.

Boson mappings and four-particle correlations in algebraic neutron-proton pairing models, J. Dobes, S. Pittel, Phys. Rev. C57 (1998) 688.

Symmetry restoration in the mean-field description of proton-neutron pairing, A.M. Romero, J. Dobaczewski and A. Pastore, Phys. Lett. B 795 (2019)177.

Heavy ion charge exchange reactions as probes for nu- clear beta -decay, Horst Lenske, Francesco Cappuzzello, Manuela Cavallaro, Maria Colonna, Prog. Part. Nucl. Phys. 109 (2019) 103716

Spin-isospin responses via (p,n) and (n,p) reactions, M. Ichimura, H. Sakai, T. Wakasa, Prog. Part. Nucl. Phys. 56 (2006) 446-531.

Charge-exchange reactions and the quest for resolution, D. Frekers and M. Alanssari, Eur. Phys. J. A 54 (2018)177.

Charge-exchange reaction cross sections and the Gamow- Teller strength for double beta decay, K. Amos, Amand Faessler and V. Rodin, Phys. Rev. C 76 (2007) 014604.

Beta decay in odd A and even even proton rich Kr isotopes, P. Sarriguren, E. Moya de Guerra, A. Escuderos, Phys. Rev. C 64 (2001) 064306.

Gamow-Teller strength distributions in Xe isotopes, O. Moreno, R. Alvarez-Rodriguez, P. Sarriguren, E. Moya de Guerra, J.M. Udias et al. Phys. Rev. C 74 (2006) 054308.

στ+ strength in nuclei, D. Cha, Phys. Rev. C 27(1983) 2269.

Comparison of Gamow-Teller strengths in the random phase approximation, Jameel-Un Nabi, Calvin W. Johnson, J. Phys. G 40 (2013) 065202.

Quasiparticle random-phase approximation with quasiparticle-vibration coupling: Application to the Gamow-Teller response of the superfluid nucleus 120 Sn, Y.F. Niu, G. Colo, E. Vigezzi, C.L. Bai, H. Sagawa, Phys.Rev.C 94 (2016) 064328.

Beta-decay properties of neutron-rich Ca, Ti, and Cr iso- topes, P. Sarriguren, A. Algora, and G. Kiss, Phys. Rev. C 98 (2018) 024311.

Nuclear spin and isospin excitations, Franz Osterfeld, Rev. Mod. Phys. 64 (1992) 491-558.

Nuclear spin and isospin excitations Franz Osterfeld, Rev. Mod. Phys. 64 (1992) 491-558.

Probing the quenching of gA by single and double beta decays, Jouni Suhonen, Osvaldo Civitarese, Phys. Lett. B 725 (2013) 153-157.

Value of the Axial-Vector Coupling Strength in β and ββ Decays: A Review, Jouni T. Suhonen, Front.in Phys. 5 (2017) 55.

Gamow-Teller strength functions and two-neutrino double- beta decay, J Hirsch, E Bauer, F Krmpotic, Nucl. Phys. A 516 (2), 304-324.

Delta excitations in nuclei and their decay properties, T. Udagawa, P. Oltmanns, F. Osterfeld, S.W. Hong, Phys. Rev. C 49 (1994) 3162-3181.

The role of the Delta in nuclear physics, G. Cattapan, L.S. Ferreira, Phys. Rep. 362 (2002) 303-407.

Gamow-Teller strength in Fe-54 and Fe-56, E. Caurier, G. Martinez-Pinedo, A. Poves, A.P. Zuker, Phys. Rev. C 52 (1995) R1736-R1740.

Discrepancy between experimental and theoretical β-decay rates resolved from first principles, Gysbers, P., Hagen, G., Holt, J.D. et al., Nat. Phys. 15, 428?431 (2019).

On the 2p-2h excitations and the quenching of the Gamow- Teller strength, J. Hirsch, A. Mariano, M. Faig, F. Krmpotik, Phys. Lett. B 210 (1988) 55-60.

Quenching of Gamow-Teller strength due to tensor corre- lations in 90Zr and 208Pb, C.L. Bai, H.Q. Zhang, X.Z. Zhang, F.R. Xu, H. Sagawa et al., Phys. Rev. C 79 (2009) 041301.

Role of momentum transfer in the quenching of Gamow- Teller strength, T. Marketin, G. Martinez-Pinedo, N. Paar, D. Vretenar, Phys. Rev. C 85 (2012) 054313.

Quenching of nuclear matrix elements for 0νββ decay by chiral two-body currents, Long-Jun Wang, Jonathan Engel, and Jiang Ming Yao, Phys. Rev. C 98 (2018) 031301(R).

Shell-model method for Gamow-Teller transitions in heavy deformed odd-mass nuclei, Long-Jun Wang, Yang Sun, and Surja K. Ghorui, Phys. Rev. C 97 (2018) 044302.

Cauldrons in the Cosmos, C.E. Rolfs, W. Rodney (Univer- sity of Chicago Press, 1988).

Frontiers in Nuclear Astrophysics, C.A. Bertulani, T. Ka- jino, Prog. Part. Nucl. Phys. 89 (2016) 56-100.

Improved estimate of electron capture rates on nuclei dur- ing stellar core collapse, A. Juodagalvis, K. Langanke, W.R. Hix, G. Mart ́ınez-Pinedo, J.M. Sampaio, Nucl. Phys. A 848 (2010) 454-478.

Nuclear spin isospin responses for low-energy neutrinos, H. Ejiri, Phys. Rep. 338 (2000) 265-351.

Neutrino-nuclear responses for astro-neutrinos, single beta decays and double beta decays, H. Ejiri, J. Suhonen, K. Zuber, Phys. Rep. 797 (2019) 1-102.

Unblocking of the Gamow-Teller strength in stellar elec- tron capture on neutron-rich germanium isotopes, K. Lan- ganke, E. Kolbe, and D. J. Dean, Phys. Rev. C 63 (2001) 032801R.

Double beta decay, T. Tomoda. Rept. Prog. Phys. 54 (1991) 53-126.

Double beta decay, Amand Faessler, Fedor Simkovic, J. Phys. G 24 (1998) 2139-2178.

Weak-interaction and nuclear-structure aspects of nuclear double beta decay, J Suhonen, O Civitarese, Phys. Rep. 300 (1998) 123-214.

The Neutrinoless double beta decay from a modern per- spective, J.D. Vergados, Phys. Rep. 361 (2002) 1-56.

The future of double beta decay research, Yu. Zdesenko, Rev. Mod. Phys. 74 (2003) 663-684.

Double beta decay, Steven R. Elliott, Jonathan Engel, J. Phys. G 30 (2004) R183-R215.

Double Beta Decay, Majorana Neutrinos, and Neutrino Mass, Frank T. III Avignone, Steven R. Elliott, Jonathan Engel, Rev. Mod. Phys. 80 (2008) 481-516.

Double Beta Decay: Historical Review of 75 Years of Re- search, A.S. Barabash, Phys. Atom. Nucl. 74 (2011) 603- 613.

Theory of Neutrinoless Double Beta Decay, J.D. Vergados, H. Ejiri, F. Simkovic, Rep. Prog. Phys. 75 (2012) 106301.

Neutrinoless Double-Beta Decay: a Probe of Physics Be- yond the Standard Model, S.M. Bilenky, C. Giunti, Int. J. Mod. Phys. A 30 (2015) 04n05, 1530001.

Status and Future of Nuclear Matrix Elements for Neu- trinoless Double-Beta Decay: A Review, Jonathan Engel, Javier Men ́endez, Rep. Prog. Phys. 80 (2017) 046301.

Weak-interaction and nuclear-structure aspects of nuclear double beta decay, J Suhonen, O Civitarese, Phys. Rep. 300 (1998) 123-214.

Shell model calculation for two neutrino double beta decay of Ca-48, L. Zhao, B.Alex Brown, W.A. Richter, Phys. Rev. C 42 (1990) 1120-1125.

A Full 0 h-bar omega description of the 2 neutrino beta beta decay of Ca-48, E. Caurier, A.P. Zuker, A. Poves, Phys. Lett.B 252 (1990) 13-17.

Neutrinoless double beta decay of Ca-48, J. Retamosa, E. Caurier, F. Nowacki, Phys. Rev. C 51 (1995) 371-378.

Shell-model calculations of two-neutrino double-beta de- cay rates of Ca-48 with GXPF1A interaction, M. Horoi, S. Stoica, B.Alex Brown, Phys. Rev. C 75 (2007) 034303.

Shell Model Analysis of the Neutrinoless Double Beta De- cay of Ca-48, Mihai Horoi, Sabin Stoica, Phys. Rev. C 81 (2010) 024321.

Shell Model Studies of the Double Beta Decays of Ge-76, Se-82, and Xe-136, E. Caurier, F. Nowacki, A. Poves, J. Retamosa, Phys. Rev. Lett. 77 (1996) 1954-1957.

Shell-Model Analysis of the 136 Xe Double Beta Decay Nuclear Matrix Elements, M. Horoi, B.A. Brown, Phys. Rev. Lett. 110 (2013) 222502.

Large-Scale Shell-Model Analysis of the Neutrinoless dou- ble beta Decay of 48Ca, Y. Iwata, N. Shimizu, T. Otsuka, Y. Utsuno, J. Men ́endez, M. Honma and T. Abe, Phys. Rev. Lett. 116 (2016) 112502.

Double Gamow-Teller Transitions and its Relation to Neu- trinoless Double Beta Decay, Noritaka Shimizu, Javier Menendez, and Kentaro Yako, Phys. Rev. Lett. 120 (2018) 142502.

Shell model Monte Carlo methods, S.E. Koonin, D.J. Dean, K. Langanke, Phys. Rep. 278 (1997) 1-77.

Suppression of the two-neutrino double-beta decay by nuclear-structure effects, P. Vogel and M. R. Zirnbauer, Phys. Rev. Lett. 57 (1986) 3148.

Nuclear structure effects in double-beta decay, J. Engel, P. Vogel, and M. R. Zirnbauer, Phys. Rev. C 37 (1988) 731.

Calculation of 2ν double beta decay of 76 Ge, 82 Se, 128,130 Te, K. Muto, H.V. Klapdor, Phys.Lett.B 201 (1988) 420-424.

Reconstruction of isospin and spin - isospin symme- tries and double beta decay, J. Hirsch, F. Krmpotic, Phys.Rev.C 41 (1990) 792-795.

Suppression of the Two Neutrino Double Beta Decay, O. Civitarese, A. Faessler, T. Tomoda, Phys. Lett. B194 ( 1987) 11-14.

ββ decay of Ge-76 with renormalized effective interaction derived from Paris, Bonn and Reid potentials, A. Staudt, T.T.S. Kuo, H.V. Klapdor- Kleingrothaus, Phys. Lett. B 242 (1990) 17-23.

Systematic approach to β and 2β decays of mass A=100- 136 nuclei, Pekka Pirinen, Jouni Suhonen, Phys. Rev. C 91 (2015) 054309.

Double Beta Decay in the Generalized Seniority Scheme, J. Engel, P. Vogel, Xiang-Dong Ji, S. Pittel, Phys. Lett. B 225 (1989) 5-9.

Suppression of the two neutrino ββ decay: Particle num- ber projected results, O. Civitarese, Amand Faessler, J. Suhonen, X.R. Wu, Phys.Lett.B 251 (1990) 333-337; Sup- pression of the two neutrino beta beta decay in a particle number projected quasiparticle random phase approxima- tion, O. Civitarese, Amand Faessler, J. Suhonen, X.R. Wu, Nucl. Phys. A 524 (1991) 404-424.

The Neutrinoless double beta decay of Ge-76, Se-82, Kr-86, Cd-114, Te-128, Te-130 and Xe-134, Xe-136 in the frame- work of a relativistic quark confinement model, J. Suho- nen, S.B. Khadkikar, Amand Faessler, Nucl. Phys. A 535 (1991) 509-547.

On the double-beta decays of Zn-70, Kr-86, Zr-94, Ru- 104, Pd-110 and Sn-124, Jouni Suhonen, Nucl. Phys. A 864 (2011) 63-90.

Review of the properties of the 0νβ−β− nuclear matrix elements, Jouni Suhonen, Osvaldo Civitarese, J. Phys. G 39 (2012) 124005.

0νββ and 2νββ nuclear matrix elements, quasiparti- cle random-phase approximation, and isospin symme- try restoration, Fedor Simkovic, Vadim Rodin, Amand Faessler, Petr Vogel, Phys.Rev.C 87 (2013) 045501.

Double beta decay to excited 0+ states: Decay of Mo-100, A. Griffiths, P. Vogel, Phys.Rev.C 46 (1992) 181-187.

Two neutrino beta beta decay to excited states: The 0+ → 2+ decay of Xe-136, J. Suhonen, O. Civitarese, Phys. Lett. B 308 (1993) 212-215.

Quasiparticle random phase approximation analysis of the double beta decay of Mo-100 to the ground state and ex- cited states of Ru-100, J. Suhonen, O. Civitarese, Phys. Rev. C 49 (1994) 3055-3060.

Two neutrino double beta decay to excited one and two phonon states, O. Civitarese, J. Suhonen, Nucl. Phys. A 575 (1994) 251-268.

Systematic study of beta and double beta decay to excited final states, M. Aunola, J. Suhonen, Nucl. Phys. A 602 (1996) 133-166.

Two neutrino double beta decay in coupled QRPA with neutron proton pairing, M.K. Cheoun, A. Bobyk, A. Faessler, F. Simkovic, G. Teneva, Nucl. Phys. A 564 (1993) 329-344.

Renormalized proton neutron quasiparticle random phase approximation and its application to double beta decay, J. Toivanen, J. Suhonen, Phys. Rev. Lett. 75 (1995) 410-413.

The Pauli principle, QRPA and the two neutrino double beta decay, J. Schwieger, F. Simkovic, Amand Faessler, Nucl.Phys.A 600 (1996) 179-192

Study of several double-beta-decaying nuclei using the renormalized proton neutron quasiparticle random-phase approximation J. Toivanen, J. Suhonen, Phys. Rev. C 55 (1997) 2314-2323.

Renormalized QRPA and double beta decay: A Critical analysis, Jorge G. Hirsch, Peter O. Hess, Osvaldo Civ- itarese, Phys. Rev. C 54 (1996) 1976-1981.

Neutron-proton correlations in an exactly solvable model, J. Engel, S. Pittel, M. Stoitsov, P. Vogel, J. Dukelsky, Phys. Rev. C 55 (1997) 1781-1788.

Single and double beta decay Fermi transitions in an ex- actly solvable model, Jorge G. Hirsch, Peter O. Hess, Os- valdo Civitarese, Phys. Rev. C 56 (1997) 199.

Critical view on double-beta decay matrix elements within quasi random phase approximation-based methods, S. Sto- ica, H.V. Klapdor-Kleingrothaus, Nucl. Phys. A 694 (2001) 269-294.

On the uncertainty in the 0νββ decay nuclear matrix el- ements, V.A. Rodin, Amand Faessler, F. Simkovic, Petr Vogel, Phys. Rev. C 68 (2003) 044302.

Assessment of uncertainties in QRPA 0νββ-decay nuclear matrix elements, V.A. Rodin, A. Faessler, F. Simkovic, P. Vogel, Nucl. Phys. A 766 (2006) 107-131, Nucl. Phys. A 793 (2007) 213-215 (erratum).

Unified description of the 2νββ decay in spherical and deformed nuclei, A.A. Raduta, A. Faessler, D.S. Delion, Nucl. Phys. A 564 (1993) 185-203.

Two neutrino double beta decay of Ge-76 within deformed GRPA: A new suppression mechanism, Fedor Simkovic, Larisa Pacearescu, Amand Faessler, Nucl. Phys. A 733 (2004) 321-350.

A Deformed QRPA formalism for single and two-neutrino double beta decay, R. Alvarez-Rodriguez, P. Sarriguren, E. Moya de Guerra, L. Pacearescu, Amand Faessler, Phys. Rev. C 70 (2004) 064309.

Two-neutrino double beta decay of deformed nuclei within QRPA with realistic interaction, Mohamed Saleh Yousef, Vadim Rodin, Amand Faessler, Fedor Simkovic, Phys. Rev. C 79 (2009) 014314

Double-beta decay in the pseudo SU(3) scheme, Octavio Castan ̃os, Jorge G. Hirsch, Osvaldo Civitarese, Peter O. Hess, Nucl. Phys. A 571 (1994) 276-300,

Neutrinoless double beta decay in heavy deformed nuclei, Jorge G. Hirsch, O. Castan ̃os, P.O. Hess, Nucl. Phys. A 582 (1995) 124-140.

Nuclear deformation and the two neutrino double-beta de- cay in Xe-124,126, Te-128,130, Ba-130-132 and Nd-150 iso- topes, S. Singh, R. Chandra, P.K. Rath, P.K. Raina, J.G. Hirsch, Eur. Phys. J. A 33 (2007) 375-388.

Nuclear deformation and neutrinoless double-beta decay of Zr-94, Zr-96, Mo-98, Mo-100, Ru-104, Pd-110, Te-128, Te-130, and Nd-150 nuclei within a mechanism involving neutrino mass, K. Chaturvedi, R. Chandra, P.K. Rath, P.K. Raina(, J.G. Hirsch, Phys. Rev. C 78 (2008) 054302.

Uncertainties in nuclear transition matrix elements for neutrinoless ββ decay within the PHFB model, P.K. Rath, R. Chandra, K. Chaturvedi, P.K. Raina, J.G. Hirsch, Phys. Rev. C 82 (2010) 064310.

Neutrinoless betaβ decay transition matrix elements within mechanisms involving light Majorana neutrinos, classical Majorons, and sterile neutrinos, P.K. Rath, R. Chandra, K. Chaturvedi, P. Lohani, P.K. Raina, Phys. Rev. C 88 (2013) 6, 064322.

Nuclear Transition Matrix Elements for Double-beta De- cay Within PHFB Model, P.K. Rath, R. Chandra, K. Chaturvedi and P.K. Raina, Front. Phys. 7 (2019) 64.

The NUMEN project: NUclear Matrix Elements for Neu- trinoless double beta decay, F. Cappuzzello, C. Agodi, M. Cavallaro, D. Carbone, S. Tudisco et al., Eur. Phys. J. A 54 (2018) 5, 72.

Pairing in nuclear systems: from neutron stars to finite nuclei, D. J. Dean, M. Hjorth-Jensen, Rev. Mod. Phys. 75 (2003) 607

Theory of Superconductivity, J. Bardeen, L.N. Cooper, and J.R. Schrieffer, Phys. Rev. 108 (1957) 1175.

Possible Analogy between the Excitation Spectra of Nuclei and Those of the Superconducting Metallic State, A. Bohr, B.R. Mottelson, and D. Pines, Phys. Rev. 110 (1958) 936.

Accuracy of the Superconductivity Approximation for Pairing Forces in Nuclei, A.K. Kerman, R.D. Lawson, M.H. Macfarlane, Phys. Rev. 124 (1961) 162-167.

Improved Superconductivity Approximation for the Pairing Interaction in Nuclei, Yukihisa Nogami, Phys. Rev. 134 (1964) B313-B321.

Conservation of Particle Number in the Nuclear Pairing Model, K. Dietrich, H.J. Mang, and J.H. Pradal, Phys. Rev. 135 (1964) B22.

A Restricted Class of Exact Eigenstates of the Pairing- Force Hamiltonian, R. W. Richardson, Phys. Lett. 3 (1963) 277-279; Exact eigenstates of the pairing-force Hamilt nian, R.W.Richardson, N.Sherman, Nucl. Phys. 52 (1964) 221-238

Exactly solvable Richardson-Gaudin models for many- body quantum systems, J. Dukelsky, S. Pittel, and G. Sierra, Rev. Mod. Phys. 76, 643-662 (2004).

Exact Solutions for Pairing Interactions, J. Dukelsky and S. Pittel, in Fifty Years of Nuclear BCS, Pairing in Finite Systems, Edited By: Ricardo A Broglia and Vladimir Zelevinsky, World Scientific, Singapore (2013), pp. 200- 211.

Exactly-solvable models derived from a generalized Gaudin algebra, G. Ortiz, R. Somma, J. Dukelsky, and S. Rom- bouts, Nucl. Phys. B 707 (2005) 421-457.

Isoscalar and Isovector Neutron-Proton Pairing, A. V. Afanasjev, in Fifty Years of Nuclear BCS, Pairing in Fi- nite Systems, Edited By: Ricardo A Broglia and Vladimir Zelevinsky, World Scientific, Singapore (2013), pp. 138- 153.

Overview of neutron-proton pairing, S. Frauendorf, A.O. Macchiavelli, Prog. Part. Nucl. Phys. 78 (2014) 24-90.

Isovector and isoscalar proton-neutron pairing in N>Z nu- clei, D. Negrea, P. Buganu, D. Gambacurta, N. Sand- ulescu, Phys. Rev. C 98 (2018) 064319.

Extension of the Shell Model for Heavy Spherical Nuclei, Michel Baranger, Phys. Rev. 120 (1960) 3, 957.

Nuclear deformations in the pairing-plus-quadrupole model, Krishna Kumar, Michel Baranger, Nucl.Phys.A 110 (1968) 529-554; Michel Baranger, Krishna Kumar, Nucl.Phys.A 122 (1968) 241-272, Nucl.Phys.A 141 (1970) 674-674 (erratum); Nuclear deformations in the pairing- plus-quadropole model (II). Discussion of the validity of the model, Michel Baranger, Krishna Kumar, Nucl.Phys.A 110 (1968) 490-528.

The pairing-plus-quadrupole model, Daniel R. Bes and Raymond A. Sorensen, M. Baranger et al. (eds.), Advances in Nuclear Physics, Plenum Press 1969, 129.

Funny Hills: The Shell-Correction Approach to Nuclear Shell Effects and Its Applications to the Fission Process, M. Brack, Jens Damgaard, A.S. Jensen, H.C. Pauli, V.M. Strutinsky et al., Rev. Mod. Phys. 44 (1972) 320-405.

Description of nuclear collective motions in terms of the boson expansion technique, T. Kishimoto, T. Tamura, Nucl. Phys. A 270 (1976) 317-380.

Interacting boson model of collective states. 1. The Vi- brational limit, A. Arima, F. Iachello, Annals Phys. 99 (1976) 253-317; Interacting boson model of collective nu- clear states. II. The rotational limit, A. Arima, F. Iachello, Annals Phys. 111 (1978) 201-238; New Symmetry in the sd Boson Model of Nuclei: The Group O(6); A. Arima, F. Iachello, Phys.Rev.Lett. 40 (1978) 385; Interacting boson model of collective nuclear states. 4. The O(6) limit, A. Arima, F. Iachello, Annals Phys. 123 (1979) 468.

Description of the Pt and Os isotopes in the interacting boson model, R. Bijker, A.E.L. Dieperink, O. Scholten, R. Spanhoff, Nucl. Phys. A 344 (1980) 207-232.

Classical limit of the interacting boson Hamiltonian, P. Van Isacker, Jin-Quan Chen, Phys. Rev. C 24 (1981) 684- 689.

Boson realizations of Lie algebras with applications to nu- clear physics, Abraham Klein, E.R. Marshalek, Rev. Mod. Phys. 63 (1991) 375-558.

The realistic collective nuclear Hamiltonian, Marianne Du- four, Andres Zuker, Phys. Rev. C 54 (1996) 1641-1660.

Spherical shell model description of rotational motion, A.P. Zuker, J. Retamosa, A. Poves, E. Caurier, Phys. Rev. C 52 (1995) R1741-R1745.

The shell model as a unified view of nuclear structure, E. Caurier, G. Mart ́ınez-Pinedo, F. Nowacki, A. Poves, and A. P. Zuker, Rev. Mod. Phys. 77 (2005) 427.

Collective motion in the nuclear shell model. 1. Classifi- cation schemes for states of mixed configuration, J.P. El- liott, Proc. Roy. Soc. Lond. A A245 (1958) 128; Collective motion in the nuclear shell model. 2. The Introduction of intrinsic wave functions, J.P. Elliott, Proc. Roy. Soc. Lond. A A245 (1958) 562-581.

Symmetries in nuclei, K.T. Hecht, Ann. Rev. Nucl. Part. Sci. 23 (1973) 123-161.

Search for a coupling scheme in heavy deformed nuclei: The pseudo SU(3) model, R.D.Ratna Raju, J.P. Draayer, K.T. Hecht, Nucl. Phys. A 202 (1973) 433-466.

Generalized pseudo-SU(3) model and pairing, D. Trolte- nier, C. Bahri, J.P. Draayer , Nucl. Phys. A 586 (1995) 53-72.

Origin of Pseudospin Symmetry, A.L. Blokhin, C. Bahri, J.P. Draayer, Phys. Rev. Lett. 74 (1995) 4149-4152.

Pseudospin symmetry in relativistic mean field theory, J. Meng, K. Sugawara-Tanabe, S. Yamaji, P. Ring, A. Arima, Phys. Rev. C 58 (1998) R628-R631.

Relativistic symmetries in nuclei and hadrons, J.N. Ginoc- chio, Phys. Rep. 414 (2005) 165-261.

Hidden pseudospin and spin symmetries and their ori- gins in atomic nuclei, Haozhao Liang, Jie Meng, Shan-Gui Zhou, Phys. Rep. 570 (2015) 1-84.

Isovectorial pairing in solvable and algebraic models, Ser- gio Lerma, Carlos E Vargas and Jorge G Hirsch, Journal of Physics: Conference Series 322 (2011) 012011,

Projected Shell Model and High-Spin Spectroscopy, Kenji Hara, Yang Sun, Int. J. Mod. Phys. E 4 (1995) 637-785.

Multiphonon gamma vibrational bands and the triax- ial projected shell model, Yang Sun, Kenji Hara, Javid A. Sheikh, Jorge G. Hirsch, Victor Velazquez et al., Phys.Rev.C 61 (2000) 064323.

Hartree-Fock-Bogolyubov calculations with the D1 effec- tive interactions on spherical nuclei, J. Decharge, D. Gogny, Phys. Rev. C 21 (1980) 1568-1593.

Coexistence in even-mass nuclei, J.L. Wood, K. Heyde, W. Nazarewicz, M. Huyse, P. van Duppen, Phys. Rep. 215 (1992) 101-201.

Theoretical Spectroscopy and the fp shell, A, Pover, A. Zuker, Phys. Rep. 70 (1981) 235-314.

Effective interaction for nuclei of A = 50-100 and Gamow- Teller properties, M Honma, T Otsuka, T Mizusaki, M Hjorth-Jensen and B A Brown, Journal of Physics: Con- ference Series 20 (2005) 2.

Full pf shell model study of A=48 nuclei, E. Caurier, A.P. Zuker, A. Poves, G. Martinez-Pinedo, Phys. Rev. C 50 (1994) 225-236.

Intrinsic vs Laboratory Frame Description of the Deformed Nucleus Cr-48, E. Caurier, J.L. Egido, G. Martinez- Pinedo, A. Poves, J. Retamosa, Phys. Rev. Lett. 75 (1995) 2466-2469.

Microscopic description of Gamow-Teller transitions in middle pf shell nuclei by a realistic shell model calcula- tion, H. Nakada, T. Sebe, J. Phys. G 22 (1996) 1349-1362.

Shell model calculations of stellar weak interaction rates: I. Gamow-Teller distributions and spectra of nuclei in the mass range A=45-65, E. Caurier, K. Langanke, G. Martinez-Pinedo, F. Nowacki, Nucl. Phys. A653 (1999) 439-452.

Evaluation of electron capture reaction rates in Ni isotopes in stellar environments, Toshio Suzuki, Michio Honma, H ́el`ene Mao, Takaharu Otsuka, and Toshitaka Kajino, Phys. Rev. C 83 (2011) 044619.

Gamow-Teller Strengths in Proton-Rich Exotic Nuclei De- duced in the Combined Analysis of Mirror Transitions, Y. Fujita, T. Adachi, P. von Brentano, G. P. A. Berg, C. Fransen, D. De Frenne, H. Fujita, K. Fujita, K. Hatanaka, E. Jacobs, K. Nakanishi, A. Negret, N. Pietralla, L. Popescu, B. Rubio, Y. Sakemi, Y. Shimbara, Y. Shimizu, Y. Tameshige, A. Tamii, M. Yosoi, and K. O. Zell, Phys. Rev. Lett. 95 (2005) 212501.

High-resolution study of Gamow-Teller transitions from the 46Ti to the Tz = 0 nucleus 46V. T. Adachi et al., Phys. Rev. C 73 (2006) 024311.

Observation of Low- and High-Energy Gamow-Teller Phonon Excitations in Nuclei, Y. Fujita et al., Phys. Rev. Lett. 112 (2014) 112502.

Tz = −1 → β decays of54Ni, 50Fe, 46Cr, and 42Tt and comparison with mirror (3He,t) measurements F. Molina et al., Phys. Rev. C 91 (2015) 014301.

Systematic shell-model study of β-decay properties and Gamow-Teller strength distributions in A ≈ 40 neutron- rich nuclei, Sota Yoshida, Yutaka Utsuno, Noritaka Shimizu, and Takaharu Otsuka, Phys. Rev. C 97 (2018) 054321.

Effective gA in the pf shell, G. Mart ́ınez-Pinedo, A. Poves, E. Caurier, and A. P. Zuker, Phys. Rev. C 53 (1996) R2602(R).

Correlation between the quenching of total GT+ strength and the increase of E2 strength, N. Auerbach, D.C. Zheng, L. II Zamick, B.Alex Brown, Phys. Lett. B 304 (1993) 17- 23.

Correlations between the quadrupole deformation, B(E2;01 → 21) value, and total GT + strength, D. Troltenier, J.P. Draayer, J.G. Hirsch, Nucl. Phys. A 601 (1996) 89-102.

Nuclear Structure Features of Gamow-Teller Excitations, Vladimir Zelevinsky, Naftali Auerbach, Bui Minh Loc, Phys. Rev. C 96 (2017) 044319.

Gamow-Teller strength distributions in fp-shell nuclei, P. B. Radha, D. J. Dean, S. E. Koonin, K. Langanke, and P. Vogel, Phys. Rev. C 56 (1997) 3079.

Shell model Monte Carlo studies of N = Z pf-shell nuclei with pairing-plus-quadrupole Hamiltonian, K. Langanke, R Vogel, Dao-Chen Zheng, Nucl. Phys, A 626 (1997) 735- 750.

Pairing and the structure of the pf-shell N Z nuclei, Alfredo Poves, Gabriel Martinez-Pinedo, Phys. Lett. B 430 (1998) 203-208.

Competition of isoscalar and isovector proton-neutron pairing in nuclei, G. Mart ́ınez-Pinedo K. Langanke, P. Vo- gel, Nucl. Phys. A 651 (1999) 379-393.

Isoscalar neutron-proton pairing and SU(4)-symmetry breaking in Gamow-Teller transitions, K. Kaneko, Y. Sun, and T. Mizusaki, Phys. Rev. C 97 (2018) 054326.

Role of T = 0 pairing in Gamow-Teller states in N = Z nuclei, C.L. Bai, H. Sagawa , M. Sasano, T. Uesaka, K. Hagino, H.Q. Zhang, X.Z. Zhang , F.R. Xu,, Phys. Lett. B 719 (2013) 116-120

Isovector spin-singlet (T = 1, S = 0) and isoscalar spin- triplet (T = 0, S = 1) pairing interactions and spin-isospin response, H Sagawa, C L Bai and G Col`o, Phys. Scr. 91 (2016) 083011 Invited Comment.

Gamow-Teller transitions and neutron-proton-pair trans- fer reactions, P. Van Isacker, A.O. Macchiavelli, Phys. Lett. B 780 (2018) 414-417.

E. Caurier, shell model code ANTOINE, IRES, Strasbourg 1989-2004.

Present Status of Shell Model Techniques, E. Caurier, F. Nowacki, Acta Physica Polonica 30 (1999) 705.

The Shell Model as Unified View of Nuclear Structure, E. Caurier, G. Martinez-Pinedo, F. Nowacki, A. Poves, A.P. Zuker, Rev. Mod. Phys. 77 (2005) 427-488.

National Nuclear Data Center, https://www.nndc.bnl.gov.

High-resolution study of Gamow-Teller excitations in the 42Ca(3He,)42Sc reaction and the observation of a low- energy super-Gamow-Teller state, Y. Fujita et. al. Phys. Rev. C 91 (2015) 064316.

High-resolution study of Tz = +2 → +1 Gamow-Teller transitions in the 44Ca(3He,)44Sc reaction, Y. Fujita et. al. Phys. Rev. C 88 (2013) 014308.

High-resolution study of Gamow-Teller transitions in the 48Ti(3He,)48V reaction, E. Ganio ̆glu et. al. Phys. Rev. C 93 (2016) 064326.

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2020-11-05

How to Cite

[1]
A. Carranza M., S. Pittel, and J. G. Hirsch, “Influence of pairing and deformation on charge exchange transitions”, Rev. Mex. Fís., vol. 66, no. 6 Nov-Dec, pp. 710–729, Nov. 2020.