Can the Neutrino tell us its Mass by Electron Capture? Amand Faessler University of Tuebingen; Heidelberg, MPI 20. May )Faessler, Gastaldo, Simkovic, J. Phys. G 42, (2015) 2)Faessler, Simkovic, Phys. Rev C91, (2015) 3)Faessler, Enss, Gastaldo, Simkovic, arXiv: Not about Experiment, the Calorimetric Detector.

Popular Public Resonance of Paper 2: Amand Faessler, University of Tuebingen Die Chemie-News hat eine Meldung mit Artikel auf Ihre Internetseite gesetzt: beim-einfang-eines-elektrons-sein-gewicht-verraten.html Das Physikportal Pro-Physik der DPG hat einen Artikel unter: beim-einfang-eines-elektrons-sein-gewicht-verraten.html Verraten_Neutrinos_beim_Einfang_ihre_Masse.html

Amand Faessler, University of Tuebingen Chemie-News: Wird das Neutrino beim Einfang eines Elektrons sein Gewicht verraten? Forscher halten nach neuen Berechnungen die Lösung einer großen Frage der Elementarteilchenphysik für möglich Physik-Portal: Verraten Neutrinos beim Einfang ihre Masse? 21. April 2015 Neuen Berechnungen zufolge kann Projekt ECHo eine der großen Fragen der Elementar­teilchen­physik klären. Popular Public Response for second Paper:

Some open problems for neutrinos: The absolute value of the anti-nueutrino mass (Mainz, Troisk: m < 2.2 eV): Beta decay of Triton (KATRIN aims at <0.2 eV). The absolute value of the neutrino mass. Electron capture in 163 Ho; ECHo (~HD-Mainz-Tü…), HOLMES (Milano Biccoca),NuMECS (Los Alamos, MSU, Central Michigan, Stanford). Dirac or Majorana particle: Neutrinoless Double Beta decay (Klapdor? + GERDA): n +n  p + p + e - + e - The Hierarchy problem: in matter;  31 = m 3 2 -m 1 2 ≠  32 = m 3 2 -m 2 2 Review Article: X. Xian, P. Vogel: Prog. Part. Nucl. Phys., June-July, 2015 Amand Faessler, University of Tuebingen

Some open problems for neutrinos: 1) The absolute value of the anti-neutrino mass? 2)The absolute value of the neutrino mass? (Topic of this talk) 3)Dirac or Majorana particle? 4)The Neutrino Hierarchy problem? Amand Faessler, University of Tuebingen

1)Mass of the Electron Anti-Neutrinos in the Tritium decay (Mainz + Troitsk, KATRIN?) With: Mass eigenstates j and flavor eigenstates e, , . Amand Faessler, University of Tuebingen

Upper limit of the Neutrino Mass in Mainz: m < 2.2 eV 95% C.L. Karlruhe KATRIN: m < 0.2 eV ?? Kurie-Plot Q = keV m 2 >0 m 2 <0 Elektronen-Energie Eur. Phys. J. C40 (2005) 447 Amand Faessler, University of Tuebingen Weinheimer

3) Dirac or Majorana Neutrinos from the neutrinoless Double Beta Decay (Klapdor et al., GERDA) P P n n Left ν Phase Space 10 6 x 2 νββ e1e1 e2e2  = c Majorana Neutrino Neutrino must have a Mass Amand Faessler, University of Tuebingen

GRAND UNIFICATION Left-right Symmetric Models SO(10) Majorana Mass: Amand Faessler, University of Tuebingen

Neutrinoless Double Beta-Decay Probability Ge 44  Se 42 Amand Faessler, University of Tuebingen T = M m

Effective Majorana Neutrino-Mass for the 0  Decay CP Tranformation from Mass to Flavor Eigenstates Time reversal CPT Amand Faessler, University of Tuebingen

Neutrino Mixing: Amand Faessler, University of Tuebingen

Neutrino Mixing Parameters X. Qian and P. Vogel, Prog. Part. Nucl. Phys. 2015, to be published. Amand Faessler, University of Tuebingen

4) Normal and inverted Hierarchy and mixing probabilities. Amand Faessler, University of Tuebingen b) Use the small energy difference between  m 2 31 = m 3 2 –m 1 2 and  m 2 32 = m 3 2 – m 2 2 a) In Matter all three flavors interact by Z 0. Only Electron-Neutrinos interact by charged current W +, W - with Electrons. e- e W e Petr Vogel et al..: Prog. Part. Nucl. Phys., July 2015.

Amand Faessler, University of Tuebingen * bound Gamow-Teller: bound electron(s1/2,p1/2) + proton [523] [h 11/2 ]7/2 -  neutron [523] [h 9/2 +f 7/2 ] 5/2 - + neutrino

Proposed by De Rujula and Lusignoli, Phys. Lett. 118B, 429 (1982). Competing Experiments with 163 Holmium in preparation: a)ECHo: Heidelberg, Mainz, Tübingen, … ; Christian Enss, Loredana Gastaldo, Blaum, Düllmann, … b) HOLMES: Milano Biccoca; Stefano Ragazzi, Angelo Nucciotti, … c) NuMECS: Los Alamos, Michigan State Univ. (NSCL), Central Michigan University, Stanford Univ. ; Gerd Kunde, … Amand Faessler, University of Tuebingen * bound

Determination of the electron neutrino mass by electron capture in Holmium + e - bound  Dysprosium* + e Amand Faessler, University of Tuebingen

Determination of the electron neutrino mass by electron capture in Holmium + e - bound  Dysprosium* + e Amand Faessler, University of Tuebingen 163 Ho M1, 3s 1/2 M2, 3p 1/ keV keV N1, 4s 1/ keV keV keV N2, 4p 1/2 O1, 5s 1/2

1) Electron at nucleus  s1/2 and p1/2 2) Electron binding energy < Q-value ≈ 2.8 [keV] For Electron Capture (in Holmium 163): Amand Faessler, University of Tuebingen E(1s 1/2, K,Ho) = 55.6 keV E(2s 1/2, L1,Ho) = 9.4 keV E(2p 1/2,L2,Ho) = 8.9 keV E(2p 3/2,L3,Ho) = 8.1 keV E(3s 1/2,M1,Ho) = 2.0 keV E(3p 1/2,M2,Ho) = 1.8 keV E(4s 1/2, N1,Ho) = 0.4 keV E(4p 1/2, N2,Ho) = 0.3 keV E(5s 1/2,O1,Ho) = 0.05 keV

Amand Faessler, University of Tuebingen r = 0  t = - ∞ ~ ln(r/r 0 )

Electron binding energies E and width  in Ho-Dy Amand Faessler, University of Tuebingen

Selfconsistent Dirac-Hartree-Fock [Grant, Desclaux and Ankudinov et al. Comp. Phys. Com. 98 (1996) 359] for 67 Ho and 66 Dy* Amand Faessler, University of Tuebingen A. Faessler, E. Huster, O. Krafft, F. Krahn, Z. Phys. 238 (1970) 352. Holmium Dysprosium

Deexcitation Spectrum (X-rays, Auger- electrons by a Calorimeter) of excited Dy* (Atom) Amand Faessler, University of Tuebingen 0 \propto G 2 weak  B f ≈ |  f (R) | 2 /|  3s1/2 (R)| 2

Spectrum of the deexcitation of one-, two- and three-hole states in 163 Dysprosium* Amand Faessler, University of Tuebingen ‚

Theoretical and experimental (ECHo) one-hole deexcitation of Dy. Amand Faessler, University of Tuebingen 3s1/2 3p1/2 4s1/2 4p1/2 5s1/2

Logarithmic10 one-hole Deexcitation Spectrum Amand Faessler, University of Tuebingen 3s1/2 3p1/2 4s1/2 4p1/2 5s1/2

If one –resonance only important at Q after folding with detector response fit theory as function of four parameters: 1) m (neutrino mass) 2) Q-E f‘ (Q-value – reson.) 3)  f‘ (width of resonance) 4) B f (intensity of resonan.) Amand Faessler, University of Tuebingen Two Resonances : fit 7 parameters Last 10 eV below the Q-value

Robertson Phys. Rev. C91, (2015) Two –Hole Spectrum; Q = 2.5 keV Amand Faessler, University of Tuebingen

Robertson [Phys. Rev. C91 (2015) 03504] takes the Two-Hole probability from Carlson and Nestor, Phys. Rev. A 8, 2887 (1973) calculated for Xe and not for Ho  Dy Sudden approximation; probability for an empty (hole ) state in Dy: ≈ Always less than 1; j = ½; 2j+1 = 2 Hole-probability: P 1-h ≈ 1 – [ ] 2(2j+1) = =  0.4 %; =  7.7 % (19 *larger) [Overlap |Z> with |Z-1>] largest difference for outside electrons. In addition to 54 Xe in 66 Dy: (6s 1/2 ) 2,(4f 5/2 ) 6, (4f 7/2 ) 4, Amand Faessler, University of Tuebingen

Difference between 54 Xenon and 67 Holmium (Literatur) 67 Ho = [ 54 Xe](6s 1/2 ) 2 (4f 5/2 ) 6 (4f 7/2 ) 5 Amand Faessler, University of Tuebingen

Our and the Robertson (arXiv: v1) 2-hole probabilities in Dy Amand Faessler, University of Tuebingen

Numerical values of Ho-Dy overlaps with holes in the selfconsitent Dirac- Hartree-Fock. A. Faessler, E. Huster, O. Krafft, F. Krahn, Z. Phys. 238 (1970) 352. Amand Faessler, University of Tuebingen Probability(Hole 4s1/2) = 0.27 % Probability(Hole 4s1/2) = 0.45 %; 66% larger

Improvement in our work over Robertson: Faessler + Simkovic, Phys. Rev. C91, (2015) 2-hole probabilities in 67 Ho and 66 Dy and not in Xe; Carlson+Nestor 1973 The electron holes ns 1/2 and np 1/2 selfconsistently in Dy (Dirac-HF) Dy has more than 8 additional 2-hole states compared to 54 Xe and not in Carlson, Nestor. For the 1-hole states the exchange and overlap corrections are included. (Bahcal 1965, Faessler 1970; not included in Vatai approximation.) Dirac-Hartree-Fock includes finite charge distribution of the nucleus. Probability for hole states ~  (n,l,j) (R) *R 2 and not at r = 0.0. Derived in second quantization: automatic antisymmetrization. New Q-value: Q = 2.8 keV. Amand Faessler, University of Tuebingen

The points are different calculations of Faessler, Huster, Krafft, Krahn: Z. Phys. 238, 352 (1970); X~ |  2s (R)/  1s (R)| 2 *overlap *exhange corrections

Amand Faessler, University of Tuebingen 1- and 2-hole excitations of our work; Q =2.8 keV 3s1/2 3p1/2 4s1/2 4p1/2 5s1/2

Probabilities for the formation of 1- and 2- hole states in Dy after electron capture in Ho. Amand Faessler, University of Tuebingen 2 ‚ ‚

Probabilities for the formation of 1- and 2- hole states in 66 Dy after electron capture in 67 Ho. Amand Faessler, University of Tuebingen ‚ Faessler, Huster, Krafft, Krahn, Z. Phys , 352 (1970)

Probability for two-hole States: Amand Faessler, University of Tuebingen Completness relation: If we apply the Vatai approximation, we obtain the same formulas for 54 Xe as Carlson and Nestor.

Probability for three-hole states Amand Faessler, University of Tuebingen 2 2

One-, two- and three-hole state deexcitation in Dy* Amand Faessler, University of Tuebingen 3s1/2 3p1/2 4s1/2 4p1/2 5s1/2 3s1/2,4s1/ keV 3s1/2,4p1/ keV 3s1/2,4p3/ keV 3s1/2, 4d3/ keV 4s1/2,4s1/ keV 4s1/2,4p1/ keV 4s1/2,4p3/ keV 4s1/2, 4d3/ keV 4s1/2, 4d5/ keV

One-, two- and three-hole deexcitation in Dy* Amand Faessler, University of Tuebingen

Finite resolution of the detector: Results near Q folded with a Gaussian 3 eV Full Width Half Maximum. Q ≈ keV.

Importance of different resonance deexcitations of Dy* at the Q value for the determination of the neutrino mass. Amand Faessler, University of Tuebingen ‚

Importance of highest two-hole state (3s 1/2, 4s 1/2 ) -1 at 2.47 keV relative to the highest one-hole state at 2.04 keV Amand Faessler, University of Tuebingen After folding theory with the spectral function of the detector fit the following 4 parameters, if only one resonance is important: 1)Neutrino mass 2)Q value:  f‘ = Q - E f‘ 3)Width of resonance  f‘ 4)Strength S ~ B f  E C = Q – E C ;  E f‘ = Q – E f‘ (3s 1/2 ) -1 (3s 1/2, 4s 1/2 ) -1

Deexcitation spectrum of 163 Dy after Electron Capture in 163 Ho with one-, two- and three- hole excitations in Dysprosium. Amand Faessler, University of Tuebingen

Compariso n with the ECHo data. Amand Faessler, University of Tuebingen Background must be included into theoretical treatment. ECHo Exp binned by 2 eV

Detailled compariso n around the 4p1/2 and 4s1/2 one-hole excitations. Amand Faessler, University of Tuebingen 4p1/2 4s1/2 Background; Configuration mixing. 4s, 4d

Summary: Determination of the electron neutrino mass by electron capture in 163Holmium? One-hole, the two-hole (for the first time correctly) and the three- hole (for the first time) deexcitation of 163 Dysprosium. Measured by the Bolometer (X-rays, Auger-electrons) Fold with Spectral Function of detector and fit 4 parameters to data one resonance: m, Q,  f‘, B f. More resonances important? Background? Conf. mixing? m determination seems to be (very) difficult but (perhaps) not impossible. Amand Faessler, University of Tuebingen THE END

Improvement for the one-hole states: Selfconsitent Dirac-Hartree-Fock for Dy with electron hole state. Faessler, Huster, Kraft, Krahn, Z. Phys. 238 (1970) 352 Exchange + overlap corrections: P p‘ (p‘ | 2 = | | 2 ×|П k=1…Z ≠f,k‘=1‘…Z‘≠p‘ | 2 (p  f‘) Typical: = and = 0.04 for (n, l, j) f‘ ≠(n,l,j) p Amand Faessler, University of TuebingenDy <Dy‘ Ho>≈0; | p f‘ P‘ f <Dy‘ f‘ f Ho>≈1 |

Improvement for the two-hole excitation in Dy compared to Hamish Robertson DHF in 67 Ho and 66 Dy and not in 54 Xe as Carlson + Nestor Holes in Dy are in the DHF iteration included selfconsistently. In 66 Dy one has more (at least 8 are important) additional two- hole states. Overlap and exchange included for the one-hole states. Charge distribution of nucleus included.  p (Nuclear radius)| 2 and not  p (r=0)| 2 weighted with r 2. Second quantization  automatic antisymmetrization Amand Faessler, University of Tuebingen

Neutrino Mass Determination: With highest energy one-hole dominance at Q  four parameters: 1) Neutrino mass, 2) Q- E b‘ (one-hole) 3)  b‘ 4) Strength b‘ Fold theory with spectral function of detector. Background; Config. Mixing ??? Fit to data. Determination of m very difficult, but (perhaps) not impossible. Amand Faessler, University of Tuebingen THE END