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

In [1]:

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

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

Out[1]:

<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 [2]:

cropped_data = data[data['Decay Times in Microseconds'] >= 0.3]
cropped_data = cropped_data[cropped_data['Decay Times in Microseconds'] <= 20]
cropped_data.describe()

Out[2]:

<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	1255.000000
mean	3.394741
std	3.877424
min	0.319997
25%	0.960000
50%	1.879998
75%	4.120002
max	19.880012

In [6]:

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)

values = np.histogram(cropped_data["Decay Times in Microseconds"], range=data_range, bins=bins)[0]
bincenters = 0.5*(bins[1:]+bins[:-1])

hist[0][0].errorbar(bincenters, values, yerr=np.sqrt(values), fmt='none', color='red')
hist[0][0].set_xlabel('Time (μs)')
hist[0][0].set_ylabel('Counts')

#hist[0][0].set_yscale('log')
values

Out[6]:

array([242, 195, 167, 101,  81,  68,  53,  52,  41,  33,  25,  19,  18,
        14,  17,   6,   5,   5,   9,   9,   8,   9,   3,   6,   3,   5,
         9,   9,   2,   2,   4,   6,   4,   5,   2,   1,   5,   8,   2,
         2,   0])

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 [5]:

line, cov = np.polyfit(bins, times, deg=1, cov=True)

coeff = unumpy.uarray(line, np.sqrt(np.diag(cov)))
coeff

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[5], line 3
      1 line, cov = np.polyfit(bins, times, deg=1, cov=True)
----> 3 coeff = unumpy.uarray(line, np.sqrt(np.diag(cov)))
      4 coeff

NameError: name 'unumpy' is not defined

In [ ]:

gamma = coeff[0]
tau = -1 / gamma
tau

Out[ ]:

2.1137124579584188+/-0.10976894836916962

In [ ]:

cropped_data_2.describe()

Out[ ]:

<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