Update description and docs
Phase space upgrad (forbidden factors)
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@@ -47,9 +47,22 @@ Deviations from linearity near the endpoint indicate:
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## Calculator Implementation
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> [!tip] Code mapping
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> Module: `beta_spectrum/components/phase_space.py` → `PhaseSpace(W0)` class
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> Module: `beta_spectrum/components/phase_space.py` → `PhaseSpace(W0, transition_type)` class
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>
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> Simple evaluation of $p \times W \times (W_0 - W)^2$ with masking near endpoint for numerical safety. Optionally includes neutrino mass support.
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> Evaluates $p \times W \times (W_0 - W)^2$ multiplied by a **transition-type-dependent forbidden factor**. Supports optional neutrino mass.
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## Transition Type and Forbidden Factors
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The `PhaseSpace` calculator accepts a `transition_type` parameter that determines the multiplicative forbidden factor applied to the baseline phase space:
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| `transition_type` | Forbidden Order | Forbidden Factor |
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|---|---|---|
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| `A`, `F1` | 0, 1 | $1$ |
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| `F1U`, `F2` | 1, 2 | $p_\nu^2 + p_e^2$ |
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| `F2U`, `F3` | 2, 3 | $p_\nu^4 + \frac{3}{10}p_\nu^2 p_e^2 + p_e^4$ |
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| `F3U`, `F4` | 3, 4 | $p_\nu^6 + 7p_\nu^4 p_e^2 + 7p_\nu^2 p_e^4 + p_e^6$ |
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The forbidden factor modifies the energy dependence of the spectrum, becoming significant at higher electron energies. See `[[10-nuclear-structure]]` for the full shape factor treatment.
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## Energy Range
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@@ -63,6 +76,6 @@ The phase space factor:
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```python
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from beta_spectrum import PhaseSpace, T_to_W
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ps = PhaseSpace(W0=T_to_W(5.0)) # endpoint = 5 MeV
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values = ps(W_grid) # returns p·W·(W₀-W)²
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ps = PhaseSpace(W0=T_to_W(5.0), transition_type="A") # allowed transition, 5 MeV endpoint
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values = ps(W_grid) # returns p·W·(W₀-W)² × forbidden_factor
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```
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