unzhakov
876e1e3ab8
- Add neutrino mass parameter to SpectrumConfig and CLI interface - Update PhaseSpace component to handle neutrino mass effects properly - Update CSV headers to show basic endpoint and all transition types - Add --csv-verbosity option to CLI with 'full' and 'concise' options - Fix comparison plots to properly show linear scale variations - Add comprehensive tests for neutrino mass functionality
49 lines
1.7 KiB
Markdown
49 lines
1.7 KiB
Markdown
# Nuclear Shell Model for β Decay
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## Overview
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The Nuclear Shell Model (NSM) is the primary theoretical framework for computing nuclear matrix elements (NMEs) in β decay. For forbidden nonunique decays like ⁹⁹Tc, the NSM computes one-body transition densities (OBTDs) that weight the single-particle transitions contributing to the decay.
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## Key Codes
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| Code | Description | Valence Spaces |
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|---|---|---|
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| NUSHELLX | Standard NSM code | Multiple (pf, sdg, etc.) |
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| KSHELL | High-performance NSM | Custom valence spaces |
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## Valence Spaces for ⁹⁹Tc
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### glekpn (Mach interaction)
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- **Protons**: 0f₇/₂, 0f₅/₂, 2p₃/₂, 2p₁/₂, 1g₉/₂
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- **Neutrons**: 0g₉/₂, 0g₇/₂, 1d₅/₂, 1d₃/₂, 2s₁/₂
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### jj45pnb (Brown-Lisetskiy interaction)
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- **Protons**: 0f₅/₂, 2p₃/₂, 2p₁/₂, 1g₉/₂
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- **Neutrons**: 0g₇/₂, 1d₅/₂, 1d₃/₂, 2s₁/₂, 0h₁₁/₂
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## OBTDs for ⁹⁹Tc
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| Transition | OBTD (glekpn) | OBTD (jj45pnb) |
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|---|---|---|
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| 1g₇/₂ → 1g₉/₂ | 0.00994 | 0.01107 |
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| 2d₅/₂ → 1g₉/₂ | 0.47752 | −0.43985 |
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**Key insight**: The dominant transition is 2d₅/₂ → 1g₉/₂ with OBTD ≈ 0.478. The jj45pnb model gives opposite sign for this transition.
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## sNME and CVC
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The small relativistic vector NME (sNME) is related to the large vector NME via the CVC hypothesis:
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```
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sNME = (R/√10) · [W₀ − (m_n − m_p) + E_C] · l-NME
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```
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where E_C is the Coulomb displacement energy. For ⁹⁹Tc, [W₀ − (m_n − m_p)] = −0.487 MeV (small Q-value makes this critical).
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## References
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- [[Shape Factor C(W, g_A)]]
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- [[SSM — Spectrum Shape Method]]
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- [[Ramalho & Suhonen (2024)]]
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- [[Song et al. (2025)]]
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