---
title: "Nuclear Structure — Overview"
date: 2026-05-14
tags:
  - beta-spectrum/nuclear-structure
status: active
aliases: [Nuclear Theory, Shape Factor, NME]
---

# Nuclear Structure Effects in β Decay

## Overview

Nuclear structure enters the β spectrum through the **shape factor** $C(Z,W)$, which encodes how the nuclear wave functions and transition matrix elements modify the spectrum beyond the point-nucleus Coulomb interaction.

## Contents

- [[nuclear-structure/01-shape-factors]] — Shape factor $C(Z,W)$: decomposition, multipole expansion, impulse approximation, induced currents

## Key Concepts

- **Shape factor decomposition:** $C(W) = g_V^2 C_V(W) + g_A^2 C_A(W) + g_V g_A C_{VA}(W)$
- **Forbidden decays:** Nonunique transitions are sensitive to $g_A$ → basis for SSM
- **sNME:** Small relativistic vector NME — critical for precision but hard to compute

## Related

- [[gA-extraction/01-ssm-algorithm]] — How to extract $g_A$ from shape factor
- [[corrections/06-recoil]] — Weak magnetism, induced currents, recoil effects