Single Particle Levels and ββ-Decay Matrix Elements in The Interacting Boson Model

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 3.0 https://creativecommons.org/licenses/by/3.0/ Single Particle Levels and ββ-Decay Matrix Elements in The Interacting Boson Model © the Authors, 2018. Published version Barea, J.; Kotila, Jenni-Mari Barea, J., & Kotila, J.-M. (2018). Single Particle Levels and ββ-Decay Matrix Elements in The Interacting Boson Model. In C. Agodi, & F. Cappuzzello (Eds.), CNNP2017 : Conference on Neutrino and Nuclear Physics (Article 012003). IOP Publishing. Journal of Physics: Conference Series, 1056. https://doi.org/10.1088/1742-6596/1056/1/012003 2018 Journal of Physics: Conference Series PAPER • OPEN ACCESS Single Particle Levels and ββ -Decay Matrix Elements in The Interacting Boson Model To cite this article: J Barea and J Kotila 2018 J. Phys.: Conf. 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Series 1056 (2018) 012003 doi :10.1088/1742-6596/1056/1/012003 Single Particle Levels and ββ-Decay Matrix Elements in The Interacting Boson Model J Barea1and J Kotila2 1Departamento de F´ısica, Universidad de Concepci´on, Casilla 160-C, Concepci´on 4070386, Chile 2University of Jyvaskyla, Department of Physics, B.O. Box 35, FI-40014, University of Jyvaskyla, Finlan E-mail: [email protected],[email protected] Abstract. Recently a new method to calculate the occupancies of single particle levels in atomic nuclei was developed in the context of the microscopic interacting boson model, in which neutron and proton degrees of freedom are treated explicitly (IBM-2). The energies of the single particle levels constitute a very important input for the calculation of the occupancies in this method, and further they play important role in the calculation of double beta decay nuclear matrix elements. Here we discuss how the 0νββ, 0νhββ, and 2νββ-decay nuclear matrix elements (NMEs) are affected when the energies of single particle levels are changed. 1. INTRODUCTION The question of whether neutrinos are Majorana or Dirac particles, and of what are their masses and phases in the mixing matrix, remains one of the most important in physics today. A direct measurement of the average mass can be obtained from the observation of the neutrinoless double beta decay, 0νββ. Several experiments are underway to detect this decay, and others are in the planning stage (for review see e.g. [1]). The half-life for this decay can be written as [τ0ν 1/2]−1=G0ν|M0ν|2|f(mi, Uei)|2,(1) where G0νis a phase space factor, M0νthe nuclear matrix element and f(mi, Uei) contains physics beyond the standard model through the masses miand mixing matrix elements Uei of neutrino species. Concomitant with the neutrinoless modes, there is also the process allowed by the standard model, 2νββ, which has been observed in several nuclei. For this process, the half-life can be, to a good approximation, factorized in the form hτ2ν 1/2i−1 =G2ν|M2ν|2.(2) In order to extract physics beyond the standard model, contained in the function fin Eq. (1), an accurate calculation of both G0νand M0νis needed. These calculations serve the purpose of extracting the neutrino mass hmνiif 0νββ is observed, and of guiding searches if 0νββ is not observed. The fact that 0νββ-decay is a unique process, and there is no direct probe which connects the initial and final states other than the process itself makes the prediction challenging for 2 1234567890 ‘’“” Conference on Neutrino and Nuclear Physics (CNNP2017) IOP Publishing IOP Conf. Series: Journal of Physics: Conf. Series 1056 (2018) 012003 doi :10.1088/1742-6596/1056/1/012003 theoretical models. Recently we have calculated the occupancies of the single particle levels in order to satisfy a twofold goal: to asses the goodness of the single particle energies and check the reliability of the used wave functions. Both tests are particularly important in the case of nuclei involved in double beta decay, as they affect the evaluation of the NMEs and then their reliability [2]. As part of the calculation single particle energies were updated as shown in Fig. 1 and further discussed in Ref. [3]. The previous and updated sets of single particle levels are obtained from the experimental excitation energies of one-particle states, but in the second case they correspond to nuclei with mass number closer to the values of the nuclei studied in this work, since we are assuming that the energies of the single particle levels change with the value of A. Due to the lack of experimental data in some cases we used interpolated values or we extract the values from systematics in several nuclei. More technical details can be found in [3]. In what follows we report the 0νββ, 0hνββ, and 2νββ-decay nuclear matrix elements calculated using these updated single particle energies. Figure 1. Comparison of previous and updated single particle energies in different shells 28-50 and 50-82 for protons and 28-50 50-82, and 82-126 for neutrons. 2. RESULTS The method of calculating ββ-decay NMEs in IBM-2 is described in detail in Refs. [4, 5] and the method for isospin restoration in Ref. [6]. The used parameters apart from single particle energies are listed in Refs. [5, 7]. 2.1. Double beta decay with light neutrino exchange, 0νββ Comparison of previous and updated 0νββ-decay NMEs calculated using IBM-2 is presented in Fig. 2. In general, the use of the updated single particle energies increase the NMEs. The 3 1234567890 ‘’“” Conference on Neutrino and Nuclear Physics (CNNP2017) IOP Publishing IOP Conf. Series: Journal of Physics: Conf. Series 1056 (2018) 012003 doi :10.1088/1742-6596/1056/1/012003 increment is especially notable in the A= 76 −100 region. These nuclei correspond to the proton shell 28-50 and neutron shells 28-50, 50-82 and Fig. 1 reveals that, indeed, the change in single particle energies is prominent in these shells. Figure 2. Comparison of previous and updated nuclear matrix elements for 0νββ-decay with light neutrino exchange calculated using IBM-2. 2.2. Double beta decay with heavy neutrino exchange, 0νhββ Fig. 3 shows the comparison of previous and updated 0νhββ-decay NMEs calculated using IBM-2. In case of heavy neutrino exchange the increase is also notable in A= 76 −100 region as in the case of light neutrino exchange, but there is a decrease in A= 150 −160 region. For A < 76, 100 <A<150, and A > 160 nuclei the NMEs stay intact, even though single particle energies are updated. Note that in Ref. [8] a method of predicting possible contributions of sterile neutrinos to neutrinoless double beta decay using 0νββ and 0νhββ NMEs was discussed. Using the NMEs obtained using updated single particle energies, also these predictions can be updated. 2.3. 2νββ-decay For comparison we also show 2νββ-decay NMEs in Fig. 4. Like in the case of light neutrino exchange, the NMEs calculated with the updated single particle energies are generally larger than the previous ones, with the notable exception of A= 116. In A= 76−100 and A= 148−160 regions the increment is notable and when combined with phase space factors, [9], will affect the predicted half-lives. Thus the extracted effective values of gAwill also be affected, if procedure of [5] is followed. 3. DISCUSSION AND SUMMARY The observed increase in the matrix elemens shown in Figures 2, 3 and 4 can be explained in our calculation scheme by considering what is affected when the single particle energies are changed. In the cases where the increase is observed the single particle energies decrease in general. This 4 1234567890 ‘’“” Conference on Neutrino and Nuclear Physics (CNNP2017) IOP Publishing IOP Conf. Series: Journal of Physics: Conf. Series 1056 (2018) 012003 doi :10.1088/1742-6596/1056/1/012003 Figure 3. Comparison of previous and updated nuclear matrix elements for 0νββ-decay with heavy neutrino exchange calculated using IBM-2. Figure 4. Comparison of previous and updated nuclear matrix elements for 2νββ-decay calculated using IBM-2. decrease or compressing of the levels produces higher values of the structure coefficients of the S and D pairs, which appear in products and raised to exponents which depends on the number of pairs or equivalently the number of bosons (see reference [4] for details). This effect is combined in protons and neutrons for A= 76−100 and only in neutrons for A= 148−160, which explains why the increasing values are at lesser extend in the last cases. Also the case A= 110 is less 5 1234567890 ‘’“” Conference on Neutrino and Nuclear Physics (CNNP2017) IOP Publishing IOP Conf. Series: Journal of Physics: Conf. Series 1056 (2018) 012003 doi :10.1088/1742-6596/1056/1/012003 affected because of the low number of protons outside closed shell. In summary, we have calculated nuclear matrix elements relevant for double beta decay (with two and zero neutrinos for light and heavy neutrino exchange) using an updated set of single particle energies which describe their measured occupancies fairly well. In some cases the new values of the matrix elements are higher than those of previous calculations, showing that the single particle level energies have an impact in our calculations, especially when both protons and neutrons are affected and the number of valence particles outside closed shells is higher. 4. ACKNOWLEDGMENTS This work was supported by Chilean Ministry of Education (Fondo Nacional de Desarrollo Cient´ıfico y Tecnol´ogico) (Grant No. 1150564) and the Academy of Finland (Suomen Akatemia) under the Finnish Center of Excellence Program 2012-2017 (Nuclear and Accelerator Based Program at JYFL). References [1] Cremonesi O and Pavan M 2014 Adv. High. Energy Phys. 2014 951432 [2] Engel J 2015 J. Phys. G: Nucl. Part. Phys. 42 034017 [3] Kotila J and Barea J 2016 Phys. Rev. C 94 034320 [4] Barea J and Iachello F 2009 Phys. Rev. C 79 044301 [5] Barea J, Kotila J and Iachello F 2013 Phys. Rev. C 87 014315 [6] Barea J, Kotila J and Iachello F 2015 Phys. Rev. C 91 034304 [7] Beller et al 2013 Phys. Rev. Lett. 111 172501 [8] Barea J, Kotila J and Iachello F 2015 2015 Phys. Rev. D 92 093001 [9] Kotila J and Iachello F 2012 Phys. Rev. C 85 034316