Implemented all planned corrections: - finite-size e/m L0 and U - atomic screening and exchange - radiative (electron only so far) Added plotter and csv_export
277 lines
149 KiB
Plaintext
277 lines
149 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "05eecb31-92a2-4304-b67b-11d524ade80c",
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"\n",
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"from beta_spectrum.components.fermi import FermiFunction\n",
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"from beta_spectrum.components.phase_space import PhaseSpace\n",
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"from beta_spectrum.components.finite_size import FiniteSizeL0\n",
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"from beta_spectrum.components.finite_size import ChargeDistributionU\n",
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"from beta_spectrum.components.screening import ScreeningCorrection\n",
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"from beta_spectrum.components.exchange import ExchangeCorrection\n",
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"from beta_spectrum.components.radiative import RadiativeCorrection\n",
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"\n",
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"from beta_spectrum.constants import ME_MEV, ALPHA, HBAR_C_MEV_FM\n",
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"\n",
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"from beta_spectrum.utils import W_to_T, T_to_W"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "9925e5cc-7029-49c9-8077-8a2b0f2875ec",
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"metadata": {},
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"outputs": [],
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"source": [
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"endpoint_MeV = 0.2953\n",
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"e_step_MeV = 0.001\n",
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"Z_d = 44\n",
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"Z_p = 43\n",
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"A = 99\n",
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"\n",
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"W0 = T_to_W(endpoint_MeV)\n",
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"E = np.arange(e_step_MeV, endpoint_MeV, e_step_MeV)\n",
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"W = T_to_W(E)\n",
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"\n",
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"F = FermiFunction(Z_d, A)\n",
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"Ph = PhaseSpace(W0=W0, m_nu=0)\n",
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"\n",
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"L0 = FiniteSizeL0(Z_d, A)\n",
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"U = ChargeDistributionU(Z_d, A)\n",
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"\n",
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"S = ScreeningCorrection(FermiFunction(Z_p, A))\n",
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"X = ExchangeCorrection(Z_p)\n",
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"\n",
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"R = RadiativeCorrection(W0)\n",
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"R_no_resum = RadiativeCorrection(W0, use_endpoint_resummation=False)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "cb986e9e-30f0-47f6-b743-ffea80b9bd9c",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"plt.plot(W, F(W))\n",
|
|
"plt.plot(W, Ph(W))\n",
|
|
"plt.yscale(\"log\")\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 4,
|
|
"id": "15f95fd3-f4a3-4753-a00c-4a876bfa54f8",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"[<matplotlib.lines.Line2D at 0x7ff67f09a660>]"
|
|
]
|
|
},
|
|
"execution_count": 4,
|
|
"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, L0(W))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 5,
|
|
"id": "3a1e2c06-4c6c-4e92-b7a9-8a8ea8d76b25",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"[<matplotlib.lines.Line2D at 0x7ff67ee6b8c0>]"
|
|
]
|
|
},
|
|
"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 0x7ff67ed44c20>]"
|
|
]
|
|
},
|
|
"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 0x7ff67ed9a660>]"
|
|
]
|
|
},
|
|
"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": [
|
|
"(1.0005, 1.577887684505027)"
|
|
]
|
|
},
|
|
"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",
|
|
"\n",
|
|
"YSCALE = \"log\"\n",
|
|
"plt.yscale(YSCALE)\n",
|
|
"if YSCALE == \"linear\":\n",
|
|
" plt.ylim(0,)\n",
|
|
"\n",
|
|
"plt.xlim(1.0005, W0)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "e3b8b2f1-51f8-4410-b7f5-c1eee57a8263",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 3 (ipykernel)",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.14.3"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|