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The β decay of the N=Z nucleus Kr72 has been studied with the total absorption spectroscopy technique at ISOLDE (CERN). A total B(GT)=0.79(4)gA2/4π has been found up to an excitation energy of 2.7 MeV. The B(GT) distribution obtained is compared with predictions from state-of-the-art theoretical calculations to learn about the ground state deformation of Kr72. Although a dominant oblate deformation is suggested by direct comparison with quasiparticle random phase approximation (QRPA) calculations, beyond-mean-field and shell-model calculations favor a large oblate-prolate mixing in the ground state ; J.A.B. acknowledges the predoctoral grant BES-2008-009412 associated with the research project FPA2007-62170 funded by Ministerio de Ciencia e Innovacion (Spain). This work has been partly supported by the Spanish Ministerio de Economía y Competitividad (MINECO) through projects FPA2012- 32443, FPA2011-24553, FPA2011-29854-C04-01, FPA2013-41267-P, FPA2014-52823-C2-1-P and FIS2011-23565, by STFC-UK (Grant No. ST/F012012/1) and by the European Union by means of the European Commission within its Seventh Framework Programme (FP7) via ENSAR (Contract No. 262010)

10 pags.; 11 figs.; 2 tabs.; PACS number(s): 23.40.Hc, 29.30.Kv, 27.50.+e, 21.10.Pc; Open Access funded by Creative Commons Atribution Licence 3.0 ; The beta decay of the N = Z nucleus Kr-72 has been studied with the total absorption spectroscopy technique at ISOLDE (CERN). A total B(GT) = 0.79(4)g(A)(2)/4 pi has been found up to an excitation energy of 2.7 MeV. The B(GT) distribution obtained is compared with predictions from state-of-the-art theoretical calculations to learn about the ground state deformation of Kr-72. Although a dominant oblate deformation is suggested by direct comparison with quasiparticle random phase approximation (QRPA) calculations, beyond-mean-field and shell-model calculations favor a large oblate-prolate mixing in the ground state. Published by the American Physical Society ; J.A.B. acknowledges the predoctoral grant BES-2008-009412 associated with the research project FPA2007-62170 funded by Ministerio de Ciencia e Innovacion (Spain). This work has ´ been partly supported by the Spanish Ministerio de Economía y Competitividad (MINECO) through projects FPA2012- 32443, FPA2011-24553, FPA2011-29854-C04-01, FPA2013- 41267-P, FPA2014-52823-C2-1-P and FIS2011-23565, by STFC-UK (Grant No. ST/F012012/1) and by the European Union by means of the European Commission within its Seventh Framework Programme (FP7) via ENSAR (Contract No. 262010) ; Peer Reviewed