On the exchange and overlap corrections in electron capture

Ватаи, Э.

doi:10.1016/0375-9474(70)90250-2

Cited by 77 publications

(76 citation statements)

References 21 publications

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“…Ho isotopes other than 163 Ho will also be produced at energies below 25 MeV, namely [160][161][162]164 Ho as shown in Figure 21 (left). For an enriched 163 Dy target, the 163 Dy(d,2n) 163 Ho reaction is found to be superior compared to the 163 Dy(p,n) 163 Ho reaction, as it provides a three times higher cross section of ∼ 900 mb at 13 MeV (Fig.…”

Section: Production Pathways For 163 Homentioning

confidence: 99%

“…In the so-called Vatai approximation [161,162] the overlaps between Ho and Dy wavefunctions with the same indices and thus identical quantum numbers are approximated by unity. In equation (27) such overlaps occur three times, namely as the second term within the parentheses and twice in the fraction (both in the nominator implicitly in B ovl j and in the denominator).…”

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confidence: 99%

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The electron capture in 163Ho experiment – ECHo

Gastaldo

Blaum

Chrysalidis

et al. 2017

Eur. Phys. J. Spec. Top.

132

110

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Abstract. Neutrinos, and in particular their tiny but non-vanishing masses, can be considered one of the doors towards physics beyond the Standard Model. Precision measurements of the kinematics of weak interactions, in particular of the 3 H β-decay and the 163 Ho electron capture (EC), represent the only model independent approach to determine the absolute scale of neutrino masses. The electron capture in 163 Ho experiment, ECHo, is designed to reach sub-eV sensitivity on the electron neutrino mass by means of the analysis of the calorimetrically measured electron capture spectrum of the nuclide 163 Ho. The maximum energy available for this decay, about 2.8 keV, constrains the type of detectors that can be used. Arrays of low temperature metallic magnetic calorimeters (MMCs) are being developed to measure the 163 Ho EC spectrum with energy resolution below 3 eV FWHM and with a time resolution below 1 μs. To achieve the sub-eV sensitivity on the electron neutrino mass, together with the detector optimization, the availability of large ultra-pure 163 Ho samples, the identification and suppression of background sources as well as the precise parametrization of the 163 Ho EC spectrum are of utmost importance. The high-energy resolution 163 Ho spectra measured with the first MMC prototypes with ion-implanted 163 Ho set the basis for the ECHo experiment. We describe the conceptual design of ECHo and motivate the strategies we have adopted to carry on the present medium scale experiment, ECHo-1K. In this experiment, the use of 1 kBq 163 Ho will allow to reach a neutrino mass sensitivity below 10 eV/c 2 . We then discuss how the results being achieved in ECHo-1k will guide the design of the next stage of the ECHo experiment, ECHo-1M, where a source of the order of 1 MBq 163 Ho embedded in large MMCs arrays will allow to reach sub-eV sensitivity on the electron neutrino mass.

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Section: Production Pathways For 163 Homentioning

confidence: 99%

mentioning

confidence: 99%

The electron capture in 163Ho experiment – ECHo

Gastaldo

Blaum

Chrysalidis

et al. 2017

Eur. Phys. J. Spec. Top.

132

110

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“…B b for the electron capture probability from the state b relative to the capture from 3s 1/2 with one hole in b' in the Dysprosium atom is given in eq. (4) in the Vatai approximation [23,24]. But the numerical value used here are calculated with the full overlap and exchange corrections of Faessler et al [5].…”

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confidence: 99%

“…But for the probability the minus sign is irrelevant. In the literature one uses often the Vatai approximation [23,24]: Exchange corrections have been neglected already in eq. (9).…”

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confidence: 99%

“…Primes always indicate states in Dy. For the probability of the second and third hole we used the so called Vatai [23,24] approximation with the overlaps of corresponding electron wave function with the same quantum numbers in Ho and Dy equal to unity and neglected the exchange corrections. For the "diagonal" overlaps of the order of ≈ 0.999 this is a good approximation.…”

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Determination of the neutrino mass by electron capture inHo163and the role of the three-hole states inDy163

et al. 2015

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Determination of the neutrino mass by electron capture in 163 Holmium and the role of the three-hole states in 163 Dysprosium. March 1, 2018Abstract 163 Ho to 163 Dy is probably due to the small Q value of about 2.5 keV the best case to determine the neutrino mass by electron capture. The energy of the Q value is distributed between the excitation of Dysprosium (and the neglected small recoil of Holmium) and the relativistic energy of the emitted neutrino including the rest mass. The reduction of the upper end of the deexcitation spectrum of Dysprosium below the Q value allows to determine the neutrino mass. The excitation of Dysprosium can be calculated in the sudden approximation of the overlap of the electron wave functions of Holmium minus the captured electron and one-, two-, three-and multiple holeexcitations in Dysprosium. Robertson [R. G. H. Robertson, Phys. Rev. C91, 035504 (2015) and arViv: 1411.2906] and Faessler and Simkovic [Amand Faessler, Fedor Simkovic, accepted for Phys. Rev. C, March 2015 and arXiv: 1501.04338] have calculated the influence of the two-hole states on the Dysprosium spectrum. Here for the first time the influence of the three-hole states on the deexcitation bolometer spectrum of 163 Dysprosium is presented. The electron wave functions and the overlaps are calculated selfconsistently in a fully relativistic and antisymmetrized DiracHartree-Fock approach in Holmium and in Dysprosium. The electron orbitals in Dy are determined including the one-hole states in the selfconsistent iteration. The influence of the three-hole states on the Dy deexcitation (by X-rays and Auger electrons) can hardly be seen. The three-hole states seem not to be relevant for the determination of the electron neutrino mass. IntroductionOne of the most pressing problems in particle physics is the determination of the absolute value of the neutrino mass. The single beta decay, specifically the Triton decay, can give the electron antineutrino mass [1] (present upper limit [2]: mν ≤ 2.2 eV ), while the neutrinoless double beta decay yields the mass of the effective Majorana electron neutrino mass [3], if the transition matrix element can be

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