BIBECHANA 19(1-2) (2022) 160-164 

 160 

 

 

Optimization of momentum of muon beam and thickness of 

cell-window for muon experiment in bio-sample: a 

simulation study 

  
Amba Datt Pant 
 

Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK),  

1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan  

Email:  pant@post.kek.jp

 

 
Article Information: 

Received: July 05, 2021 

Accepted: December 31, 2021 

 

 

Keywords:  

Muon 

Muonium 

Kapton 

Cancer 

Bio-samples 

Muon spin rotation  

Relaxation  

 

 

 
 

ABSTRACT 

In order to study the bio-samples (aqueous solutions) using muon spin 

rotation and relaxation (SR) method, the optimization of momentum of 

incident muon beam and selection of material for window of sample cell 

towards muon side are the initial steps for the SR measurement. Rather than 

several experimental trials, we used to perform simulation study to optimize 

the momentum of muon beam and thickness of window of the sample cell. 

Monte Carlo simulation for optimization of momentum of monoenergetic 

surface muon beam in different material/thickness of window of the sample 

cell indicates that the Al or Kapton window of thickness less than 0.3 mm is 

suitable to maximize the intensity of the stopped muons (momentum between 

25.8 MeV/c to 29.8 MeV/c) within 1 mm of water (bio-samples). This 

simulation will help to design the sample cell for the study of application of 

muon in life science. 

  
 

 
DOI: https://doi.org/10.3126/bibechana.v19i1-2.46413 
 

This work is licensed under the Creative Commons CC BY-NC License. 

https://creativecommons.org/licenses/by-nc/4.0/ 

BIBECHANA 
ISSN 2091-0762 (Print), 2382-5340 (Online) 

Journal homepage: http://nepjol.info/index.php/BIBECHANA 

Publisher: Department of Physics, Mahendra Morang A.M. Campus, TU, Biratnagar, Nepal 

https://doi.org/10.3126/bibechana.v19i1-2.46413
https://creativecommons.org/licenses/by-nc/4.0/


Amba Datt Pant / BIBECHANA 19(1-2) (2022) 160-164 

 

 

 161 

1. Introduction 

 

Muon spin rotation and relaxation (SR) 

method is being popular for study of life and 

materials. In this method, decay positron from 

the muon can be detected by spectrometer 

around the sample and the information about 

the desired properties of the material can be 

extracted from the time evolution of muon 

spectra [1]. Since muon is like a light proton, 

and its bound state with an electron is like a 

light isotope of hydrogen atom, this method 

can be used to understand the local electronic 

and dynamics states of the materials. Not 

limited to materials and life science [2-4], the 

muon can be used for discovery of new physics 

beyond standard model, nuclear physics, 

advancement of technology, etc [5]. In order to 

apply the muon to understand the properties of 

materials, it should be stopped in the sample 

material and the background should be 

minimized. Selection of proper momentum of 

muon beam and optimization thickness of 

window of sample cell (especially for bio-

samples) are preliminary and the most 

important steps in this method. For the 

experiments to be performed in high vacuum 

and samples in which different muon charge 

states will be expected, especial care should be 

taken to select/use the material for sample cell.  

Muon is an elementary particle which is like 

a light proton (m ~ 1/9 mp;  = 3.18 p) and 

sensitive to magnetic field. For SR 

experiment, high intensity muons can be 

generated in accelerator facilities however it is 

also possible to perform SR studies using 

cosmic muons. Because of fully polarized and 

asymmetric decay to positron, it is used as 

promising tool to study the local electronic and 

dynamic states of materials in which it stops. 

Moreover, its unique and wide time window (~ 

ps to few s) provides more advantages over 

other resonance techniques (NMR, ESR, 

Mössbauer, etc.) [1, 6]. When muon incident 

in sample, based on nature/properties of 

samples, muon can be found as diamagnetic 

muon, muonium or other states in the sample. 

After its average life 2.2 s, it decays to 

positron along the direction of muon spin at the 

time of decay. Such positrons are collected by 

the detectors installed around the sample. The 

time evolution of polarization provides the 

information about the materials. So the SR 

method has been used in wide varieties of 

samples without any external perturbations [1]. 

In our previous study of application of muon 

for cancer study, we have used decay muon of 

momentum of 60 MeV/c at RIKEN/RAL, UK 

[7-9]. For such beam, bio-samples of around a 

liter volume were used. As a next step, we plan 

to perform experiment in small and real bio-

samples rather than dilute aqueous solutions. 

For such purpose, the low momentum muon 

(surface muon of momentum ~ 29 MeV/c) will 

be used at J-PARC, Japan. Before such 

experiments, it is necessary to optimize the 

thickness of windows of sample cell and 

momentum of muon beam so that muon can 

stopped in the targeted region of sample. In this 

work, the Monte Carlo simulation study to 

optimize the momentum of muon beam and 

thickness of sample cell-window to maximize 

the stopped muon in the targeted sample is 

presented. 

 

2. Methodology 

Based on materials and thickness of sample 

cell-window (Fig. 1), the incident 

monoenergetic surface muon beam stops in 

window materials and/or sample. To 

optimize/estimate the thickness of the sample 

cell-window and momentum of muon beam, 

the Stopping and Range of Ions in Matter 

(SRIM-2013) Monte Carlo simulations code 

[10, 11] were used. The momentum and energy 

of surface muon beam are 29.79 MeV/c and 

4.119 MeV, respectively [12]. Based on 

transportation of beam in beamlines, the real 

momentum will be less than the 29.79 MeV/c. 

 
Fig. 1. Schematic diagram of 

incident of muon beam in bio-

sample. 



Amba Datt Pant / BIBECHANA 19(1-2) (2022) 160-164 

 

 

 162 

So, the simulations were performed at different 

momentum and materials. Among them three 

momentum data in two materials – aluminum 

(Al) and Kapton have been discussed here. In 

simulation, water is used instead of bio-sample 

because the aqueous bio-sample or real bio-

sample some extent of water exists. The 

density of water is less than that of bio-sample 

so the stopping information in water is fine for 

bio-samples. 

The Al of density 2.7 g/cc and Kapton of 

density 1.42 g/cc were used in simulation. The 

Kapton is polyimide which is used for different 

purposes – electric and thermal insulation, 

windows for high vacuum, protection layer, etc. 

The intensity of incident muon was taken over 

at least 104 events. 

3. Results and Discussion 

 

The simulation of muon stopping in both Al 

and Kapton sheets of different thicknesses 

have been performed at three different 

momentum of monoenergetic surface muon 

beam. Figure 2 shows the stopping range of 

muon in water. Even the muon beam of 

momentum 25.79 MeV/c can pass the 0.1 mm 

(Fig. 2(a)) and 0.3 mm (Fig. 2 (b)) of Al cell-

window. However, in the case of 0.4 mm 

thickness (Fig. 2 (c)), a small fraction (< 1% of 

incident muon) of 25.79 MeV/c muon stopped 

in the window. Furthermore, in the case of 0.5 

mm thickness (Fig. 2 (d)), all the 25.79 MeV/c 

muon stopped in the window.   

The muon of momentum 25.79 MeV/c, 

27.79 MeV/c and 29.79 MeV/c passes through 

the Kapton windows and stopped in water are 

presented in Fig. 3. In the case of Kapton 

thickness 0.05 mm (Fig. 3(a)) and 0.4 mm (Fig. 

(b)), all muons stopped in water within 2 mm 

depth. When the thickness of Kapton is 

increases to 0.6 mm, only small fraction (< 1% 

of incident muon) of muon of 25.79 MeV/c 

stopped in the Kapton window. In the case of 

thickness 0.8 mm (Fig. 3(c)), the 25.79 MeV/c 

muon stopped in the Kapton however other 

higher momentum muon passed the window 

and stopped in the water. 

With regard to monoenergetic muon beam, 

 
Fig. 2. Stopping range of muon beam of different momentum passed through the Al window in 

water (a) Al windows thickness, t = 0.1 mm, (b) t = 0.3 mm, (c) t = 0.4 mm and (d) t = 0.5 mm. The 

light blue color for water and light silver color for Al are used. The line colors blue, black and red 

are used for momentum of muon beam 25.79 MeV/c, 27.79 MeV/c and 29.79 MeV/c, respectively.     



Amba Datt Pant / BIBECHANA 19(1-2) (2022) 160-164 

 

 

 163 

the stopping range difference for particular 

thickness is smaller (full width at half 

maximum is smaller) however in real beamline 

there is certain distribution of muon energy. In 

such cases low energy muon may stop in the 

window materials. For this reason, the 

selection of cell-window is quite important. If 

the muon stopped in window material, there is 

possibility of background or noise signal from 

the charge states of muon stopped in the 

windows materials. For example, muon 

stopped in Kapton (unsaturated organic 

material) may form radical or muonium state 

however in Al there will be muon in 

diamagnetic state. 

For the selection of windows material, we 

also need to consider about the visualization of 

sample for example during experiments using 

light/laser or if we use other visual 

spectroscopic detectors during SR 

experiment. For such purpose, the window of 

Kapton or glass will be better than Al. In 

addition, the chemical reaction of bio-sample 

with those window material should also be 

considered. For real bio-sample, the density 

will be different than the water used in this 

study. So, the density of particular sample also 

should be taken into account before selection 

of the cell window. 

 

Conclusion  

The stopping range of surface muon in 

different thickness of Al and Kapton window 

of sample cell for SR experiment in bio-

sample cell have been studied using Monte 

Carlo simulation. Optimization of thickness of 

the window and momentum of muon beam 

shows that the thickness of Al or Kapton 

window within 0.3 mm will suitable to pass the 

muon beam of momentum between 25.79 

MeV/c and 29.79 MeV/c. The thickness of 

windows suggested by this study will be used 

in the experiments to be performed in future 

SR experiments in aqueous biological 

samples. 

 

Acknowledgment  

This work was supported by Grant-in-Aid 

for Scientific Research of the Ministry of 

 
Fig. 3. Stopping range of muon beam of different momentum passed through the Kapton window in 

water (a) Kapton windows thickness, t = 0.05 mm, (b) t = 0.4 mm, (c) t = 0.6 mm and (d) t = 0.8 

mm. The light blue color for water and light pink for Kapton are used. The line colors blue, black 

and red are used for momentum of muon beam 25.79 MeV/c, 27.79 MeV/c and 29.79 MeV/c, 

respectively. 



Amba Datt Pant / BIBECHANA 19(1-2) (2022) 160-164 

 

 

 164 

Education, Culture, Sports, Science and 

Technology (MEXT), Japan, (Grant Number: 

21K15583, “Applications of muon in cancer 

research”). 

 

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