notes-archive/statics/physics/modern-phys-lab/decay.ipynb

In [11]:

import matplotlib.pyplot as plt
import numpy as np
import pandas

data = pandas.read_csv('20250212_EC_decays.txt')
data.describe()

Out[11]:

<style scoped=""> .dataframe tbody tr th:only-of-type { vertical-align: middle; } .dataframe tbody tr th { vertical-align: top; } .dataframe thead th { text-align: right; } </style>

	Decay Times in Microseconds
count	1257.000000
mean	3.421448
std	3.931721
min	0.319997
25%	0.960001
50%	1.880002
75%	4.120004
max	20.319996

In [20]:

cropped_data = data[data['Decay Times in Microseconds'] >= 0.3]
cropped_data = cropped_data[cropped_data['Decay Times in Microseconds'] <= 20]
cropped_data.describe()
hist = cropped_data.hist(range=data_range, bins=bins)

In [15]:

data_range = (0.3, max(data['Decay Times in Microseconds']))
bins = np.arange(0.3, max(data['Decay Times in Microseconds']) + 0.5, 0.5)
hist = cropped_data.hist(range=data_range, bins=bins)
hist[0][0].set_yscale('log')

In [4]:

cropped_data_2 = cropped_data[cropped_data['Decay Times in Microseconds'] <= 7]
data_range = (0.3, max(cropped_data_2['Decay Times in Microseconds']))
bins = np.arange(0.3, max(cropped_data_2['Decay Times in Microseconds']) + 0.5, 0.5)
hist = cropped_data_2.hist(range=data_range, bins=bins)
hist[0][0].set_yscale('log')

times, bins = np.histogram(cropped_data_2, bins=bins, range=data_range)
times = np.log(times)
bins = bins[:-1]

In [ ]:

line = np.polynomial.polynomial.Polynomial.fit(bins, times, deg=1)
line=line.convert()

Out[ ]:

$x \mapsto \text{5.62523946} - \text{0.47310125}\,x$

In [30]:

gamma=line.convert().coef[1]
tau = -1/gamma
tau

Out[30]:

np.float64(2.113712457958419)

In [22]:

cropped_data_2.describe()

Out[22]:

<style scoped=""> .dataframe tbody tr th:only-of-type { vertical-align: middle; } .dataframe tbody tr th { vertical-align: top; } .dataframe thead th { text-align: right; } </style>

	Decay Times in Microseconds
count	1102.000000
mean	2.161488
std	1.617221
min	0.319997
25%	0.879998
50%	1.640000
75%	3.040010
max	6.960006