From 0c5c53688d2b56e05b683c8929e343bd0e794af1 Mon Sep 17 00:00:00 2001
From: Evgeniy Unzhakov <unzhakov_ev@pnpi.nrcki.ru>
Date: Fri, 10 Apr 2026 15:32:47 +0300
Subject: [PATCH] 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/__init__.py               |  19 +-
 beta_spectrum/components/exchange.py    |  66 +++++++
 beta_spectrum/components/fermi.py       |  15 +-
 beta_spectrum/components/finite_size.py |  40 +++++
 beta_spectrum/components/radiative.py   | 148 ++++++++++++++++
 beta_spectrum/components/screening.py   |  97 +++++++++++
 beta_spectrum/constants.py              |   3 +-
 beta_spectrum/units.py                  |  12 --
 beta_spectrum/utils.py                  |  20 ++-
 notebooks/testing.ipynb                 | 222 ++++++++++++++++++++----
 pyproject.toml                          |   4 +-
 11 files changed, 580 insertions(+), 66 deletions(-)
 create mode 100644 beta_spectrum/components/exchange.py
 delete mode 100644 beta_spectrum/units.py

diff --git a/beta_spectrum/__init__.py b/beta_spectrum/__init__.py
index 4f767ae..767c8b6 100644
--- a/beta_spectrum/__init__.py
+++ b/beta_spectrum/__init__.py
@@ -1,17 +1,30 @@
 # beta_spectrum/__init__.py
 
-from .constants import ALPHA
-from .units import T_to_W, W_to_T
+from .constants import ALPHA, HBAR_C_MEV_FM, ME_MEV, MP_MEV
+from .utils import T_to_W, W_to_T, momentum
 
 from .components.phase_space import PhaseSpace
 from .components.fermi import FermiFunction
+from .components.finite_size import FiniteSizeL0, ChargeDistributionU
+from .components.screening import ScreeningCorrection
+from .components.exchange import ExchangeCorrection
+from .components.radiative import RadiativeCorrection
 
 __all__ = [
     "ALPHA",
+    "HBAR_C_MEV_FM",
+    "ME_MEV",
+    "MP_MEV",
     "T_to_W",
     "W_to_T",
+    "momentum",
     "PhaseSpace",
     "FermiFunction",
+    "FiniteSizeL0",
+    "ChargeDistributionU",
+    "ScreeningCorrection",
+    "ExchangeCorrection",
+    "RadiativeCorrection",
 ]
 
-__version__ = "0.1.0"
+__version__ = "0.1.1"
diff --git a/beta_spectrum/components/exchange.py b/beta_spectrum/components/exchange.py
new file mode 100644
index 0000000..32262fc
--- /dev/null
+++ b/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
diff --git a/beta_spectrum/components/fermi.py b/beta_spectrum/components/fermi.py
index d0657ec..2fe2bc4 100644
--- a/beta_spectrum/components/fermi.py
+++ b/beta_spectrum/components/fermi.py
@@ -19,7 +19,7 @@ class FermiFunction(SpectrumComponent):
         p = np.sqrt(W**2 - 1.0)
 
         # Avoid division by zero
-        p = np.where(p == 0, 1e-30, p)
+        p = np.clip(p, 1e-30, None)
 
         eta = self.alphaZ * W / p
 
@@ -36,17 +36,12 @@ class FermiFunction(SpectrumComponent):
         log_gamma_complex = loggamma(z)
         log_gamma_abs_sq = 2 * np.real(log_gamma_complex)
 
-        log_gamma_denom = 2 * loggamma(2 * self.gamma + 1).real
+        log_gamma_denom = 2 * np.real(loggamma(2 * self.gamma + 1))
 
         # log exponential
         log_exp = np.pi * eta
 
-        logF = (
-            log_prefactor
-            + log_power
-            + log_gamma_abs_sq
-            - log_gamma_denom
-            + log_exp
-        )
+        logF = log_prefactor + log_power + log_gamma_abs_sq - log_gamma_denom + log_exp
+
+        return np.exp(logF)
 
-        return np.exp(logF)
\ No newline at end of file
diff --git a/beta_spectrum/components/finite_size.py b/beta_spectrum/components/finite_size.py
index 0a91382..8648e34 100644
--- a/beta_spectrum/components/finite_size.py
+++ b/beta_spectrum/components/finite_size.py
@@ -2,3 +2,43 @@ import numpy as np
 
 from beta_spectrum.constants import ALPHA
 from beta_spectrum.base import SpectrumComponent
+from beta_spectrum.utils import nuclear_radius
+
+
+class FiniteSizeL0(SpectrumComponent):
+    """
+    Finite nuclear size correction L0(W)
+
+    Implements low-Z expansion (Hayen et al.)
+    Includes (1 + gamma)/2 prefactor
+    """
+
+    def __init__(self, Z: int, A: int):
+        self.Z = Z
+        self.A = A
+
+        self.R = nuclear_radius(A)
+
+        self.alphaZ = ALPHA * Z
+        self.gamma = np.sqrt(1 - self.alphaZ**2)
+
+        # beta-minus decay
+        self.sign = -1
+
+    def __call__(self, W: np.ndarray) -> np.ndarray:
+        # Terms from expansion
+        term1 = self.sign * self.alphaZ * W * self.R
+        term2 = (13 / 60) * self.alphaZ**2
+        term3 = -0.5 * (self.alphaZ * self.R) / W
+
+        return 1 + term1 + term2 + term3
+
+
+class ChargeDistributionU(SpectrumComponent):
+    def __init__(self, Z: int, A: int):
+        self.Z = Z
+        self.R = nuclear_radius(A)
+        self.alphaZ = ALPHA * Z
+
+    def __call__(self, W: np.ndarray) -> np.ndarray:
+        return 1.0 + (1 / 5) * (self.alphaZ * W * self.R) ** 2
diff --git a/beta_spectrum/components/radiative.py b/beta_spectrum/components/radiative.py
index e69de29..de21026 100644
--- a/beta_spectrum/components/radiative.py
+++ b/beta_spectrum/components/radiative.py
@@ -0,0 +1,148 @@
+import numpy as np
+from scipy.special import spence
+
+from beta_spectrum.base import SpectrumComponent
+from beta_spectrum.constants import MP_MEV, ME_MEV, ALPHA
+
+
+class RadiativeCorrection(SpectrumComponent):
+    """
+    Outer radiative correction R(W, W0) = 1 + delta(W, W0).
+
+    Implements Eq. (47)-(50) from Hayen et al. 2017, with endpoint
+    divergence handeled by the soft photon resummation of Eq. (53).
+
+    This is the INCLUSIVE correction suitable for:
+    - Magnetic spectrometers
+    - Detectors where bremmstrahlung is not detected
+    - Precision at 1% level or worse
+    """
+
+    def __init__(self, W0: float, use_endpoint_resummation: bool = True):
+        """
+        Args:
+            W0: Endpoint energy in natural units m_e=c=h_bar=1
+            use_endpoint_resummation: Apply eq. (53) to handle ln(W0 - W) divergence
+        """
+        self.W0 = W0
+        self.use_endpoint_resummation = use_endpoint_resummation
+        self.m_p = MP_MEV / ME_MEV  # ~1836.15
+
+        # Precompute constant terms of Eq. (48)
+        self._outer_normalization = ALPHA / (2.0 * np.pi)  # ~0.00116
+        self._subtraction_term = 3.0 * np.log(self.m_p / (2.0 * self.W0))
+
+    def __call__(self, W: np.ndarray) -> np.ndarray:
+        """
+        Calculate R(W, W0) = 1 + delta_R(w, W0)
+
+        Args:
+            W: Electron total energy array (in natural m_e=c=h_bar=1 units)
+
+        Returns:
+            Radiative correction factor array
+        """
+        W = np.asarray(W)
+
+        # Avoid numerical issues exactly at enpoint W0
+        eps = 1e-9
+        mask_finite = W < (self.W0 - eps)
+
+        delta_R = np.zeros_like(W, dtype=float)
+
+        if np.any(mask_finite):
+            W_finite = W[mask_finite]
+
+            if self.use_endpoint_resummation:
+                g_func = self._g_function_resummed(W_finite)
+            else:
+                g_func = self._g_function_standard(W_finite)
+
+            delta_R_finite = self._outer_normalization * (
+                g_func - self._subtraction_term
+            )
+            delta_R[mask_finite] = delta_R_finite
+
+        # Apply full correction including inner and L factor
+        return 1.0 + delta_R
+
+    def _g_function_standard(self, W: np.ndarray) -> np.ndarray:
+        """
+        Standard delta_R from Eq. (50), without endpoint resummation.
+        Has logarithmic divergence as W -> W0
+        """
+        beta = np.sqrt(1.0 - 1.0 / W**2)
+        beta = np.maximum(beta, 1e-12)  # Avoid division by 0
+
+        # Dilogarithm term
+        arg = 2.0 * beta / (1.0 + beta)
+        arg = np.minimum(arg, 1.0 - 1e-12)  # Avoid numerical problems at arg=1
+        dilog_term = (4.0 / beta) * spence(arg)
+
+        # arctanh factor
+        atanh_beta = np.arctanh(beta)
+        atanh_factor = (atanh_beta / beta) - 1.0
+
+        # Energy difference
+        delta_W = self.W0 - W
+        delta_W = np.maximum(delta_W, 1e-12)
+
+        # Second line Eq. (50)
+        term2 = 4.0 * atanh_factor * (delta_W / (3.0 * W) - 1.5 + np.log(2.0 * delta_W))
+
+        # Third line Eq. (50)
+        term3 = (atanh_beta / beta) * (
+            2.0 * (1.0 + beta**2) + (delta_W**2) / (6.0 * W**2) - 4.0 * atanh_beta
+        )
+
+        # Leading constants from Eq. (50)
+        const_term = 3.0 * np.log(self.m_p) - 0.75
+
+        return const_term + dilog_term + term2 + term3
+
+    def _g_function_resummed(self, W: np.ndarray) -> np.ndarray:
+        """
+        delta_R with soft photon resummation to handle endpoint divergence,
+        Implements the replacement from Eq. (53):
+
+        t(beta) * ln(W0 - W) -> (W0 - W)^t(beta) - 1
+        """
+        beta = np.sqrt(1.0 - 1.0 / W**2)
+        beta = np.maximum(beta, 1e-12)
+
+        # t(beta) from Eq. (54)
+        atanh_beta = np.arctanh(beta)
+        t_beta = (2.0 * ALPHA / np.pi) * (atanh_beta / beta - 1.0)
+
+        # Dilogarithm term (same as _delta_R_standard)
+        arg = 2.0 * beta / (1.0 + beta)
+        arg = np.minimum(arg, 1.0 - 1e-12)
+        dilog_term = (4.0 / beta) * spence(arg)
+
+        # arctanh factor
+        atanh_factor = (atanh_beta / beta) - 1.0
+
+        # Energy difference
+        delta_W = self.W0 - W
+        delta_W = np.maximum(delta_W, 1e-12)
+
+        # Apply resummation from Eq. (53)
+        # Replace divergent ln(W0 - W) term with (W0 - W)^t(beta) - 1
+        resummed_log_term = (delta_W**t_beta) - 1.0
+
+        # Term2 with resummed log (instead of ln(2*(W0 - W)))
+        term2_resummed = (
+            4.0
+            * atanh_factor
+            * (delta_W / (3.0 * W) - 1.5 + 0.5 * resummed_log_term + np.log(2.0))
+        )
+
+        # Term3 (no divergence)
+        term3 = (atanh_beta / beta) * (
+            2.0 * (1.0 + beta**2) + (delta_W**2) / (6.0 * W**2) - 4.0 * atanh_beta
+        )
+
+        # Leading constants
+        const_term = 3.0 * np.log(self.m_p) - 0.75
+
+        return const_term + dilog_term + term2_resummed + term3
diff --git a/beta_spectrum/components/screening.py b/beta_spectrum/components/screening.py
index e69de29..5e3391c 100644
--- a/beta_spectrum/components/screening.py
+++ b/beta_spectrum/components/screening.py
@@ -0,0 +1,97 @@
+import numpy as np
+
+from beta_spectrum.base import SpectrumComponent
+from beta_spectrum.utils import momentum
+from beta_spectrum.constants import ALPHA
+
+
+class ScreeningCorrection(SpectrumComponent):
+    """
+    Atomic screning correction S(Z, W).
+
+    Implements:
+        - Ratio method (non-screened to screened F(Z,W)*p*W) using shifted energy W -> W_tilde
+        - Smooth switching function to regularize low-energy behaviour
+
+    S(W) = 1 + f(W) * (S_raw(W) - 1
+    """
+
+    def __init__(
+        self,
+        fermi_function,
+        V0: float = None,
+        Ws: float = 1.01,
+        Delta: float = 0.005,
+        eps: float = 1e-6,
+        C=0.015,
+    ):
+        """
+        Parameters
+        ----------
+        Z : nuclear charge
+        fermi_function : callable
+            Instance of FermiFunction class
+        V0 : screening potential (in m_e units)
+            If None, uses simple scaling law
+        Ws : switching midpoint
+        Delta : switching width
+        eps : numerical floor for W_tilde
+        """
+        self.fermi = fermi_function
+        self.Z = fermi_function.Z
+        self.Ws = Ws
+        self.Delta = Delta
+        self.eps = eps
+        self._C = C
+        self.V0 = V0 if V0 is not None else self._estimate_V0()
+
+    # --------------------
+    # Core evaluation
+    # --------------------
+    def __call__(self, W: np.ndarray) -> np.ndarray:
+        W = np.asarray(W)
+
+        # Energy shift by screening potential V0
+        W_tilde = self._screened_energy(W)
+
+        # Momenta
+        p = momentum(W)
+        p_tilde = momentum(W_tilde)
+
+        # Fermi functions
+        F = self.fermi(W)
+        F_tilde = self.fermi(W_tilde)
+
+        # Raw ratio model (for W >> V0)
+        S_raw = (F_tilde / F) * (p_tilde * W_tilde) / (p * W)
+
+        # Smooth switching
+        f = self._switching_function(W)
+
+        return 1.0 + f * (S_raw - 1.0)
+
+    # --------------------
+    # Helpers
+    # --------------------
+    def _screened_energy(self, W):
+        """
+        Apply energy shift W -> W_tilde with safe numerical floor
+        """
+        W_tilde = W - self.V0
+        return np.maximum(W_tilde, 1.0 + self.eps)
+
+    def _switching_function(self, W):
+        """
+        Logistic switching function
+        """
+        return 1.0 / (1.0 + np.exp((self.Ws - W) / self.Delta))
+
+    def _estimate_V0(self):
+        """
+        Simple scaling estimate for screening potential.
+
+        V0 ~ alpha * Z^(4/3) * C
+
+        C ~ 0.01-0.02 (tunable constant)
+        """
+        return ALPHA * self.Z ** (4.0 / 3.0) * self._C
diff --git a/beta_spectrum/constants.py b/beta_spectrum/constants.py
index c76ee44..f5be66d 100644
--- a/beta_spectrum/constants.py
+++ b/beta_spectrum/constants.py
@@ -1,4 +1,5 @@
 # constants.py
 ALPHA = 1 / 137.035999084  # fine-structure constant
 HBAR_C_MEV_FM = 197.3269804  # MeV * fm
-ME_MEV = 0.510998950  # MeV
+ME_MEV = 0.510998950  # MeV / c^2
+MP_MEV = 938.272088816  # MeV / c^2
diff --git a/beta_spectrum/units.py b/beta_spectrum/units.py
deleted file mode 100644
index 0fb0adc..0000000
--- a/beta_spectrum/units.py
+++ /dev/null
@@ -1,12 +0,0 @@
-# units.py
-import numpy as np
-
-ME_KEV = 510.99895000  # keV electron mass
-
-
-def W_to_T(W: float | np.ndarray) -> np.ndarray:
-    return (W - 1.0) * ME_KEV
-
-
-def T_to_W(T_keV: float | np.ndarray) -> np.ndarray:
-    return T_keV / ME_KEV + 1.0
diff --git a/beta_spectrum/utils.py b/beta_spectrum/utils.py
index 3dc2c14..324fe0b 100644
--- a/beta_spectrum/utils.py
+++ b/beta_spectrum/utils.py
@@ -1,9 +1,27 @@
 # utils.py
+import numpy as np
+
 from .constants import HBAR_C_MEV_FM, ME_MEV
 
 
-def nuclear_radius(A: float) -> float:
+def nuclear_radius(A: float, r0: float = 1.2) -> float:
     r0_fm = 1.2  # fm
     R_fm = r0_fm * A ** (1 / 3)
 
     return R_fm / (HBAR_C_MEV_FM / ME_MEV)
+
+
+def momentum(W):
+    return np.sqrt(W**2 - 1)
+
+
+def neutrino_energy(W, W0):
+    return W0 - W
+
+
+def W_to_T(W: float | np.ndarray) -> np.ndarray:
+    return (W - 1.0) * ME_MEV
+
+
+def T_to_W(T_keV: float | np.ndarray) -> np.ndarray:
+    return T_keV / ME_MEV + 1.0
diff --git a/notebooks/testing.ipynb b/notebooks/testing.ipynb
index c9d8228..0ce19be 100644
--- a/notebooks/testing.ipynb
+++ b/notebooks/testing.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 1,
    "id": "05eecb31-92a2-4304-b67b-11d524ade80c",
    "metadata": {},
    "outputs": [],
@@ -11,31 +11,55 @@
     "import matplotlib.pyplot as plt\n",
     "\n",
     "from beta_spectrum.components.fermi import FermiFunction\n",
-    "from beta_spectrum.components.phase_space import PhaseSpace"
+    "from beta_spectrum.components.phase_space import PhaseSpace\n",
+    "from beta_spectrum.components.finite_size import FiniteSizeL0\n",
+    "from beta_spectrum.components.finite_size import ChargeDistributionU\n",
+    "from beta_spectrum.components.screening import ScreeningCorrection\n",
+    "from beta_spectrum.components.exchange import ExchangeCorrection\n",
+    "from beta_spectrum.components.radiative import RadiativeCorrection\n",
+    "\n",
+    "from beta_spectrum.utils import W_to_T"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 2,
    "id": "9925e5cc-7029-49c9-8077-8a2b0f2875ec",
    "metadata": {},
    "outputs": [],
    "source": [
-    "W = np.linspace(1.001, 2.0, 1000)\n",
+    "W0 = 1.574\n",
+    "Z = 44\n",
+    "A = 99\n",
     "\n",
-    "F = FermiFunction(Z=44, A=99)\n",
-    "Ph = PhaseSpace(W0=2.0, m_nu=0)"
+    "W = np.linspace(1.001, W0, 1000)\n",
+    "\n",
+    "F = FermiFunction(Z, A)\n",
+    "Ph = PhaseSpace(W0=W0, m_nu=0)\n",
+    "\n",
+    "L0 = FiniteSizeL0(Z, A)\n",
+    "U = ChargeDistributionU(Z, A)\n",
+    "\n",
+    "S = ScreeningCorrection(F)\n",
+    "X = ExchangeCorrection(Z)\n",
+    "\n",
+    "R = RadiativeCorrection(W0)\n",
+    "R_no_resum = RadiativeCorrection(W0, use_endpoint_resummation=False)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 3,
    "id": "cb986e9e-30f0-47f6-b743-ffea80b9bd9c",
-   "metadata": {},
+   "metadata": {
+    "jupyter": {
+     "source_hidden": true
+    }
+   },
    "outputs": [
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -46,28 +70,6 @@
    ],
    "source": [
     "plt.plot(W, F(W))\n",
-    "plt.yscale(\"log\")\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "id": "33ec0920-1c16-4a4d-8abf-befb4764d15d",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
     "plt.plot(W, Ph(W))\n",
     "plt.yscale(\"log\")\n",
     "plt.show()"
@@ -75,13 +77,23 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
-   "id": "c550cc3c-130e-4959-aa05-82f1c2b10fa7",
+   "execution_count": 4,
+   "id": "15f95fd3-f4a3-4753-a00c-4a876bfa54f8",
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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",
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7f9eafcea660>]"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -91,10 +103,146 @@
     }
    ],
    "source": [
-    "plt.plot(W, F(W) * Ph(W))\n",
-    "# plt.yscale(\"log\")\n",
-    "plt.show()"
+    "plt.plot(W, L0(W))"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "3a1e2c06-4c6c-4e92-b7a9-8a8ea8d76b25",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7f9eafcbbcb0>]"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.plot(W, U(W) - 1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "b58c605b-4ece-4434-a880-c4f0ab221fa2",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7f9eafa69010>]"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.plot(W, S(W))\n",
+    "plt.plot(W, X(W))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "cdf7950e-7960-4369-8639-4d8b1995b9e1",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7f9eafaf5a90>]"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.plot(W, R(W))\n",
+    "plt.plot(W, R_no_resum(W))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "b67a9c5c-af77-4b4f-ac04-2b8705a85125",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7f9eafb63230>]"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.plot(W, Ph(W)*F(W)*L0(W)*U(W)*S(W)*X(W)*R(W))\n",
+    "plt.plot(W, Ph(W)*F(W)*L0(W)*U(W)*S(W)*X(W)*R_no_resum(W))\n",
+    "plt.plot(W, Ph(W)*F(W))\n",
+    "# plt.yscale(\"log\")\n",
+    "# plt.xlim(1.0005,)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "e3b8b2f1-51f8-4410-b7f5-c1eee57a8263",
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
diff --git a/pyproject.toml b/pyproject.toml
index 2c75dee..7312a97 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -4,10 +4,10 @@ build-backend = "setuptools.build_meta"
 
 [project]
 name = "beta-spectrum"
-version = "0.1.0"
+version = "0.1.1"
 description = "High-precision beta spectrum calculation for nuclear physics"
 authors = [
-    { name = "Your Name" }
+    { name = "Evgeniy Unzhakov" }
 ]
 requires-python = ">=3.10"