MVP Correction Implemented

Add implementation for the basic set of spectrum components:

Primary
-------
- Phase Space
- Fermi Function

Corrections
-----------

- Atomic:
  - Screening
  - Atomic exchange
- E/M and finite size:
  - Finite nucleus size and charge distribution
  - Radiative

beta_spectrum/components/exchange.py

@@ -0,0 +1,66 @@
+from pathlib import Path
+import numpy as np
+from beta_spectrum.base import SpectrumComponent
+
+
+class ExchangeCorrection(SpectrumComponent):
+    """
+    Atomic xchange correction using Hayen 2018 Table X coefficients (App. G)
+    """
+
+    def __init__(self, Z: int, filename=None, eps: float = 1e-6):
+        self.Z = Z
+        self.eps = eps
+
+        if filename is None:
+            filename = self._default_coeff_path()
+
+        self.coeffs = self._load_coeffs(filename)
+
+    def _load_coeffs(self, filename):
+        data = np.genfromtxt(filename, delimiter=",", names=True)
+
+        for row in data:
+            if int(row["Z"]) == self.Z:
+                return {
+                    "a": row["a"],
+                    "b": row["b"],
+                    "c": row["c"],
+                    "d": row["d"],
+                    "e": row["e"],
+                    "f": row["f"],
+                    "g": row["g"],
+                    "h": row["h"],
+                    "i": row["i"],
+                }
+        raise ValueError(f"No exchange coefficients available for Z={self.Z}")
+
+    def _default_coeff_path(self):
+        return Path(__file__).resolve().parent.parent / "data" / "exchange_coeff.csv"
+
+    def __call__(self, W: np.ndarray) -> np.ndarray:
+        W = np.asarray(W)
+
+        # W' = W - 1 (threshold-sensitive)
+        Wp = np.maximum(W - 1.0, self.eps)
+
+        a = self.coeffs["a"]
+        b = self.coeffs["b"]
+        c = self.coeffs["c"]
+        d = self.coeffs["d"]
+        e = self.coeffs["e"]
+        f = self.coeffs["f"]
+        g = self.coeffs["g"]
+        h = self.coeffs["h"]
+        i = self.coeffs["i"]
+
+        # Terms
+        term1 = a / Wp
+        term2 = b / (Wp**2)
+        term3 = c * np.exp(-d * Wp)
+
+        # Numerical safe (W - f)^g
+        base = np.maximum(W - f, self.eps)
+        term4 = e * np.sin((base**g + h)) / (W**i)
+
+        return 1.0 + term1 + term2 + term3 + term4