Bull. Soc. Photogr. Imag. Japan. (2022) Vol. 32 No. 1: 10–14

Original Paper

Energy Uncertainties of Charged Particles with Respect to the Density Error andRange Straggling in Nuclear Emulsion Sheet
Phyo Myat Lina*, Ayumi KASAGIa,c, Kazuma NAKAZAWAa,b, Naoki NISHIMURAb, Aung Nay Lin Nyawb,
Junya YOSHIDAc,d, Masahiro YOSHIMOTOe

Abstract:

Alpha particle tracks resulting from the decay of natural radioisotopes have been used as a reference for the energy calibration of charged particles in nuclear emulsion sheets. The suitable number of alpha tracks to yield the minimized mass error of the double hypernucleus calculated
from kinetic energy errors, which related to the density errors of emulsion layer, was determined. The results showed that at least 150 alphatracks were sufficient to utilize in the calibration. The kinetic energy error from range straggling was also determined and was one order greater than that from the density error of emulsion layer.

Key words:

Double hypernuclei, Nuclear emulsion sheet, Density of emulsion layer, Range‒energy relation, and Energy‒calibration source

1. Introduction
The objective of our research is to understand baryon‒baryon interactions in double strangeness systems by investigating the characteristics of a double hypernucleus, which has two strange quarks.
Particularly, we study Ξ hyperon ‒ nucleon (Ξ-Ν) interaction and Λ
hyperon ‒ Λ hyperon (Λ-Λ) interaction. Hypernuclei have a very
short lifetime, and they can traverse only a few micrometers fromthe production point in a medium. Consequently, nuclear emulsion
sheets, which have a submicrometer spatial resolution, were used forthe study of hypernuclei over the last five decades.1) We can trace thetrajectories of all charged particles passing through a nuclear emulsion sheet. A theoretical calculation suggests that hyperons may appear in the core of a neutron star at a density several times higher
than the nuclear saturation density (ρ0≈0.17fm-3).2) Therefore, byunderstanding the Ξ-Ν and Λ-Λ interactions, we can obtain information on the structure of the interior core of a neutron star. The
Ξ-Ν and Λ-Λ interactions were reported with typical events such as
NAGARA3), KISO4,5), and KINKA6) events in the nuclear emulsion
sheet of the KEK PS-E373 (E373) experiment, and MINO7), IBUKI8), D0019), IRRAWADDY6), T0076), and T0116) events in that of
the J-PARC E07 (E07) experiment. The most recent experiment,
E07, aimed to detect nearly 100 events of double hypernuclei and
identify the decay modes of 10 events among them uniquely. Thusfar, 33 events of double hypernuclei were detected in the first-orderanalysis of the E07 experiment. Details of the production of nuclear

emulsion sheets and the experimental setup for E07 were reported
by Nyaw et al.9) and Ekawa et al.7). To obtain knowledge of Ξ-Ν andΛ-Λ interactions without any ambiguity arising from the differencesin the core nuclei, it is extremely important to observe uniquely
identified events independent of the reported events. In the near
future, we are upgrading the scanning system to detect more eventsof double hypernuclei in the nuclear emulsion sheet of the E07 experiment.
The accuracy of range measurement is one of the main concepts
to get minimize energy error on analyzing hypernuclear events.
However, the track ranges of charged particles recorded in the emulsion sheet at beam exposure time and after photographic development are not the same because the thickness of emulsion layer isshrunk after the development process and the density of emulsion
layer changes. Therefore, alpha tracks that have monochromatic energy were used to calibrate the density of emulsion layer. This paper
will report how many numbers of alpha tracks are sufficient for thecalibration to obtain reasonable energy error.

2. Theory
2.1 Range-energy (RE) relation
To calculate the Ξ-Ν and Λ-Λ interactions, it is necessary to know
the mass of double hypernuclei. The mass can be obtained by measuring the kinetic energy (KE) at the decay of daughter particles.
The KE is converted from the range of charged particles in the

Received 24th December, 2021; Accepted 6th May, 2022; Published 10th May, 2022a) Graduate school of Engineering, Gifu University, Gifu 501-1193, Japanb) Graduate school of Education, Gifu University, Gifu 501-1193, Japanc) High Energy Nuclear Physics Laboratory, Cluster for Pioneering Research, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japand) Department of Physics, Tohoku University, Sendai 980-8578, Japane) RIKEN Nishina Center for Accelerator-Based Science, RIKEN, 2-1 Hirosawa, Wako, Saitama 351- 0198, Japan* maphyomyatlin@gmail.com

Phyo Myat Lin, Ayumi KASAGI, Kazuma NAKAZAWA, Naoki NISHIMURA, Aung Nay Lin Nyaw, Junya YOSHIDA, Masahiro YOSHIMOTO

emulsion sheet by the following range‒energy (RE) relation10):. ( )+=,(1)
where R and Z represent the range and charge of particles, respectively. M is the mass of charged particles in proton mass units. Cz isan empirical function to correct range extension, which was experiβ
for various nuclei. In this case,mentally estimated as a function of ─Zλ(β) is the range of protons at velocity βc in the emulsion layer of theE07 experiment, which is expressed as 11)
( )

=

+

(

)

.

,

(2)
where λs and λw are proton ranges in the standard emulsion layer
and water, respectively. Further, ds and d are the densities of the standard emulsion layer (3.815 g.cm-3) and the emulsion layer used in
the current experiment, respectively; r is the ratio increment of thevolume to weight caused by the absorption of moisture in the emulsion layer.
A nuclear emulsion sheet is made up of emulsion gel with a dispersion of silver halide crystal and polystyrene film base. To visualize
the tracks of charged particles in the emulsion sheet with microscopes, a photographic development was performed after beam exposure. In the development process, a fixation process to remove
undeveloped silver halide was also applied in order to prevent image
degradation. After photographic development, the thickness of
emulsion layer was reduced to nearly one-half of the original thickness due to the removal of silver halide, which can be represented as
shrinkage factor (S). Therefore, the calibration of the density ofemulsion layer by the use of alpha tracks of several tens number ineach emulsion sheet is important to get the optimal RE relation.
Alpha tracks from the natural radioisotopes of the thorium series
and uranium series have been used as energy‒calibration sources tocalibrate the density change of emulsion layers for the last half-century. The superimposed images of alpha tracks in the emulsion sheet
are shown in Fig. 1. Conventionally, alpha-decay events are searchedby visual inspection; however, this method needs enormous effort.
Although the relation between the number of alpha-decay eventsand the error of mass reconstruction is important, it has not been
sufficiently studied. In the recent past, a new technique called Overall scanning was developed to detect alpha tracks from the wholevolume of an emulsion layer in a reasonable time.12) Recently, Yoshida et al. employed the convolutional neural network to classify alpha-decay events in nuclear emulsion sheets13). Using the methods
developed for searching alpha-decay events, we can investigate a

Fig. 1 Superimposed images of alpha tracks generated by the decay of (a)thorium series and (b) uranium series.

Energy Uncertainties of Charged Particles with Respect to the Density Error and Range Straggling in Nuclear Emulsion Sheet11

sufficient number of alpha tracks to estimate the corresponding energy error.
On measuring the range of charged particles in the nuclear emulsion sheet, an error called range straggling arises and affects the masserror of the double hypernucleus. This error of range straggling (∆R)
is a statistical error, and it can be calculated by the following equation as a function of KE14):

(

)=

.

,

(3)
where ∆Rp represents the error of range straggling by the proton.
The KE and kinetic energy error (KEerr) from density error of emulsion layer (derr) and error of range straggling will be described in alater part of this paper.
2.2 Calibration
For the calibration of density of emulsion layer, the alpha track
generated by the decay of 212Po in the thorium series, which had thelongest track and a monochromatic energy of 8.785 MeV was applied. The average range of alpha track was calculated using the
track's length in the three-dimensional Cartesian coordinates by thefollowing equation:

=

+

+(

) ,

(4)
where Rα is a range of alpha tracks; ∆X =∑ (xi+1-xi)2 ;∆Y 2=∑ni=1(yi+1-yi)2 ; ∆Z 2=∑ni=1(zi+1-zi)2 ; i is the i-th measurement point
on a track; and S is the shrinkage factor in the z-direction, which isthe same direction of the layer thickness and also the light axis of an
optical microscope. To determine the value of S that gives an appropriate R of charged particles, ranges of the alpha track were initiallycalculated by varying S from 1.75 to 2.10 at intervals of 0.0025.
Then, the appropriate S was adopted when the range distribution ofalpha tracks for various angles has the minimum standard deviation(Min_Stdev) to provide an optimal mean range (MR). The error ofmean range (MRerr) was calculated by multiplying the standard deviation (Stdev) of alpha track ranges with the inverse square root of
the total number of alpha tracks. Fig. 2 (a) shows the standard deviation corresponding to S and (b) shows the distribution of the range
2

n
i=1

Fig. 2 Alpha range calibration. (a) The appropriate shrinkage factor S
was extracted where the minimum standard deviation Stdev ofrange distribution. (b) Alpha track range distribution with theappropriate shrinkage factor.

12Bull. Soc. Photogr. Imag. Japan. Vol. 32 No. 1 (2022)

using the determined value of S.

3. Analysis
3.1 Determination of ranges
To determine a sufficient number of alpha tracks for the calibration, alpha-decay events from three emulsion sheets, namely, PL#02, #03, and #04 from Module #030 of the E07 experiment, wereused. Around 500 alpha-decay events from each emulsion sheet
were considered. Thus, we obtained S as 1.9650, 1.9225, and 1.7875
for PL #02, #03, and #04, respectively. Then, MR ± MRerr for PL#02, #03, and #04 were 49.95 ± 0.05, 49.89 ± 0.06, and 49.55 ±0.05 μm, respectively. To confirm the consistency of the range distributions for three emulsion sheets, we applied the chi-square test fornormal distributions, as shown in Fig. 3. The calculated chi-squarevalues of the alpha track range distribution for PL #02, #03, and #04
were 27.37, 21.27, and 26.29, respectively, with a degree of freedom(DOF) of 29. All the p-values for the three emulsion sheets are

Fig. 3 Alpha range distributions for PL #02, #03, and #04. All alphatracks are in the range of 46‒54 μm. The fitting distributionfunction represented with a solid line is Gaussian.
Table 1 Calculated densities of emulsion layer from three areas labeled AC, ALU, and ALD of PL #05 from theModule #030 of J-PARC E07 experiment.

Area [cm2]
AC (5cm*10cm)

Number ofd [g⸳cm−3] derr [g⸳cm−3]alpha tracks

ALU (5cm*10cm)
ALD (5cm*10cm)

150

3.558

0.012

150

3.565

0.013

150

3.562

0.013

greater than the 0.05 level of significance (p = 0.552, 0.849, and
0.610 for PL #02, #03, and #04, respectively). Therefore, the range
distribution is sufficiently approximated by the normal distribution.
This result indicates that the ranges of alpha tracks in the threeemulsion sheets are consistent.
3.2 Measurement of density of emulsion layer
Before determining the sufficient number of energy‒calibration
sources, the uniformity of density of emulsion layer in one sheet waschecked by using alpha tracks from three areas; near the center (AC),left up corner (ALU), and left down corner (ALD) of PL #05 from
Module #030 of the E07 experiment. The number of alpha tracks
from areas AC, ALU, and ALD were 213, 209, and 259, respectively. To
check the density uniformity in one sheet, the densities and density
errors of emulsion layer for each area were calculated by using 150
alpha tracks that are randomly selected from each area as listed inTable 1. Therefore, the densities of emulsion layer in one emulsion
sheet are uniform within 1σ of the measurement error.
3.3 Optimum count number of alpha tracks
To determine the sufficient number of alpha tracks, firstly, theranges of alpha tracks were calculated using randomly selected number of alpha tracks from each emulsion sheet (PL #02, #03, and #04).
These alpha tracks were categorized into six groups of 10, 50, 100,
150, 200, and 250 tracks (i.e., groups classified with total track number to G-10, G-50, G-100, G-150, G-200, and G-250, respectively).
Then, densities and density errors of emulsion layer for each groupare calculated with the obtained mean range of alpha tracks. As
shown in Table 2, d for the six groups vary from 3.574 to 3.643
g･cm-3 and they are uniform within 3σ in three sheets. The averageof derr decreased with an increase in the count number from G-10 toG-100, and it seemed to be saturated from G-150 to G-250. Therefore, it may be sufficient to take at least 150 alpha tracks for calibration.
3.4 Error calculation
Relationships between KE and KEerr of charged particles wereanalyzed and number of alpha tracks to be counted were examinedfrom the calculated d and derr values. Since the range distributions forthree emulsion sheets were normally distributed and the obtained
densities of emulsion layer were uniformed within 3σ, we took an
approximate value (d0) as 3.6 g･cm-3 for the KE and KEerr calculations from averages for six groups in Table 2. The average ofTable 2 The d and derr for the groups with a different number of alpha tracks taken from three emulsion sheets.
The unit is g･cm-3.

Number of
10
50
100
150
200
250
alpha tracks
Density and
d
derr
d
derr
d
derr
d
derr
d
derr
d
derr
Density error
PL #02
3.617 0.0473 3.589 0.0217 3.596 0.0142 3.596 0.0113 3.575 0.0100 3.595 0.0091
PL #033.574 0.0474 3.609 0.0215 3.589 0.0157 3.579 0.0120 3.604 0.0113 3.586 0.0093

PL #043.613 0.0520 3.643 0.0177 3.624 0.0130 3.626 0.0096 3.619 0.0085 3.607 0.0077

Average

3.601 0.0489 3.613 0.0203 3.603 0.0143 3.600 0.0110 3.600 0.0099 3.596 0.0087

Phyo Myat Lin, Ayumi KASAGI, Kazuma NAKAZAWA, Naoki NISHIMURA, Aung Nay Lin Nyaw, Junya YOSHIDA, Masahiro YOSHIMOTO

Energy Uncertainties of Charged Particles with Respect to the Density Error and Range Straggling in Nuclear Emulsion Sheet

13

Fig. 4 Relationships between kinetic energy (KE) and kinetic energy error (KEerr) of the particles for six groups (G-10, G-50,
G-100, G-150, G-200, and G-250). (a) For the proton and (b) for three kinds of particles; proton, 4He, and 7Li.

the KEerr obtained from ∆R was also calculated. To compare the
KEerr values obtained from the density error of emulsion layer and∆R, KE was varied from 0.5 to 100 MeV at intervals of 0.25 MeV.
We used derr_avg of G-150 for the calculation of KEerr. Fig. 5 showsthat the KEerr from ∆R is one order of magnitude larger than thatfrom derr_avg for five particles, namely, the proton, 4He, 7Li, 9Be, and11
B.

4. Conclusion

Fig. 5 Comparison of KEerr value for each KE obtained from (a) ∆R
and (b) derr_avg for proton, 4He, 7Li, 9Be, and 11B.

derr(derr_avg) was taken from the same number of groups for each
emulsion sheet.
The range of proton was calculated by setting d0 for the region
where KE values were varied from 0 to 100 MeV at an interval of
10 MeV. Then, KEerr for three charged particles (proton, alpha (4He),
and lithium (7Li)) were calculated using obtained range, d0, andderr_avg of each group. Relationships between KE and KEerr for proton
in each group are shown in Fig. 4(a). The gaps of KEerr in the groups
G-10, G-50, G-100, and G-150 to the group of G-150, G-200, and
G-250 are large. As shown in Fig. 4(b), tendencies of KEerr gap for4
He and 7Li are similar to those for the proton, although there were
small differences in KEerr among the referred particles. According tothese results, we decided that utilizing at least 150 alpha tracks forthe calibration was sufficient.
Although Table 2 indicates that the densities of emulsion layer
varied from 3.574 to 3.643 g･cm-3, we set d0 as 3.6 g･cm-3 for thecalibration. Therefore, we calculated the KEerr variation by changing
d0 with ± 0.1 g･cm-3, where the density error of emulsion layer was
set to be derr_avg. As a result, the maximum ratio of the difference toKEerr was ± 2.35% (0.004 MeV) for the proton of 100 MeV. The
heavier particles have smaller ratios than that of proton. The deviation generated by changing d0 with ± 0.1 g･cm-3 was sufficiently
small to be ignored.
As ∆R is a statistical error in the analysis of double hypernuclei,

We decided that it was sufficient to use 150 alpha tracks for density calibration because there were small KEerr gaps among G-150,
G-200, and G-250. We also checked that the KEerr from ∆R is oneorder larger than that from derr_avg. Recently, 33 events of double hypernuclei were detected from the first analysis of the E07 experiment, and only six events have been analyzed and published. This
study intends to provide a further analysis scheme of the double
hypernuclei that may be detected in the E07 experiment in the future as well as the remaining events to obtain a reasonable energy
error from the density error of emulsion layer.

Acknowledgements

The authors would like to thank the members of the J-PARC
accelerator and the Hadron experimental facility for their experimental support for the E07 experiment. We would also like to express our gratitude to the members of the Kamioka Observatory,
ICRR, for maintaining our emulsion sheets in the Kamioka mine toprevent cosmic rays. This work was supported by Japan Society for
the Promotion of Science ( JSPS) KAKENHI grant numbers
23224006, JP16H02180, and JP20H00155, and Ministry of Education, Culture, Sport, Science and Technology (MEXT) KAKENHI
grant numbers 15001001 (Priority Area), 24105002, JP18H05403
and JP19H05417 (Innovative Area 2404).

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