4.6 KiB
4.6 KiB
title, date, tags, status, aliases, cssclasses
| title | date | tags | status | aliases | cssclasses | |||
|---|---|---|---|---|---|---|---|---|
| Hayen et al. (2017) — Reference Metadata | 2026-04-26 |
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active |
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Hayen et al. (2017) — "Beta-decay spectrum shape"
Citation
L. Hayen, K. Haseroth, N. Severijns, W. H. E. Schwarz, Rev. Mod. Phys. 90, 015008 (2018).
DOI: 10.1103/RevModPhys.90.015008
PDF Location
~/LBML_cloud/ОПЯД/beta_corrections/Refs/Hayen2017.pdf (2.1 MB, 63 pages)
Summary: ~/wiki_brain/beta_shape/Hayen2017_summary.md
Key Equations Reference
| Eq # | Section | Description | Wiki Note |
|---|---|---|---|
| (1)–(5) | II | Dirac radial wave functions, Coulomb phase | 01-fermi-function |
| (6) | II.2 | Fermi function F_0(Z,W) |
01-fermi-function |
| (7) | III | Phase space factor | 02-phase-space |
| (9)–(15) | IV.A | Finite size: uniform sphere, Coulomb energy | 03-finite-size |
| (16) | IV.A.1 | L_0(Z,W) — finite size correction to Fermi function |
03-finite-size |
| (17)–(24) | IV.A.2 | Modified Gaussian charge distribution, fit parameters | 03-finite-size |
| (25), (29) | IV.B | U(Z,W) — diffuse nuclear surface correction |
03-finite-size |
| (40) | IV.C | DFS — deformation correction to electrostatic potential |
03-finite-size |
| (41)–(45) | V | Recoil kinematic corrections, weak magnetism terms | 07-recoil-effects |
| (46)–(47) | VI.A | Radiative corrections \delta_R'(W,W_0), Sirlin g(W_0,W) |
06-radiative-corrections |
| (53) | VI.A.2 | Soft-photon resummation (W_0-W)^{t(\beta)} - 1 |
06-radiative-corrections |
| (78)–(81) | VII.A | Multipole expansion, form factors F_{KLs}, impulse approximation |
10-nuclear-structure |
| (83), (92)–(104) | VI.E | Shape factor C(Z,W) in Holstein notation |
10-nuclear-structure |
| (107) | VI.G | \Lambda factor for ft value analysis, weak magnetism contribution |
07-recoil-effects |
| (113) | VI.F | Isovector correction C_I(Z,W) — isospin symmetry breakdown |
11-isospin-breakdown |
| (140), (144) | VII.A.2 | Atomic screening S_{\text{Sal}}(Z,W) with Salvat potential |
04-screening-correction |
| (157) | VII.E.3 | Analytical fit for exchange correction X(Z,W) |
05-exchange-correction |
| (160), (163), (164) | VII.C–D | Shake-up, shake-off processes | 12-atomic-overlap, 11-isospin-breakdown |
| (166) | VII.D | Bahcall atomic mismatch correction r(Z,W) |
12-atomic-overlap |
| (171) | VII.E | Bound state β decay branching ratio \Gamma_b/\Gamma_c |
12-atomic-overlap |
| (176) | VII.F.3 | Molecular screening correction \Delta S_{\text{Mol}} |
13-chemical-effects |
| (178) | IX | Normalized shape factor S(W) for BSM searches |
07-recoil-effects |
Table References
| Table | Content | Wiki Note |
|---|---|---|
| I | Leptonic radial wave function expansion coefficients | — |
| II | Leptonic and nuclear quantum numbers, multipole classification | 10-nuclear-structure |
| III | Form factor mapping BB ↔ HS notation | 10-nuclear-structure |
| IV | Numerical values for L_0 correction (Z=2–54) |
03-finite-size |
| V | Nuclear matrix element operators (M_F, M_{GT}, etc.) |
10-nuclear-structure |
| VI | Numerical values for screening correction S(Z,W) at 67.2 keV (Ni) |
04-screening-correction |
| VII | Complete overview of all β spectrum shape corrections | 00-beta-spectrum-overview |
Key Numbers to Remember
- Target precision:
10^{-4}down to 1 keV for low-to-medium Z nuclei - Exchange correction: Can exceed 20% at low energy for high Z (Table X, Eq. 157)
- Radiative corrections: Sirlin's
g(W_0,W)diverges logarithmically at endpoint → handled via soft-photon resummation - Induced pseudoscalar
g_P(0): PCAC predicts ~−229 for free nucleon, quenched by up to 80% in nuclear medium - Weak magnetism uncertainty: Can shift
f_A/f_Vvalues by several parts in10^3
Crosschecks in Paper
- Superallowed Fermi decays (§VIII): Excellent agreement with Towner & Hardy (2015) f values, all residuals in few
\times 10^{-4}region - Mirror decays: Exquisite agreement for vector sector (<
4\times 10^{-4}); axial vector depends on nuclear model choice
Related Notes
- 00-beta-spectrum-overview — Master equation and full corrections table (Table VII)
- 10-nuclear-structure — Shape factor formalism, BB vs HS comparison (§E in paper)
- 07-recoil-effects — Recoil kinematics, weak magnetism, induced currents