Proposal for Measurement of the Two-body Neutron Decay using Microcalorimeter Shuo Zhang1yXavier Mougeot2Song-Lin Wang3Jian-Rong Zhou3 Wen-Tao Wu4Jing-Kai Xia1Rui-Tian Zhang5and Le Zhang6

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Proposal for Measurement of the Two-body Neutron Decay using Microcalorimeter∗

Shuo Zhang,1, †Xavier Mougeot,2Song-Lin Wang,3Jian-Rong Zhou,3

Wen-Tao Wu,4Jing-Kai Xia,1Rui-Tian Zhang,5and Le Zhang6

1Center for Transformative Science, ShanghaiTech University, ShangHai, 201210, China

2CEA, LIST, Laboratoire National Henri Becquerel, CEA-Saclay, Gif-sur-Yvette Cedex,91191, France

3Institute of High Energy Physics, Chinese Academy of Sciences, BeiJing, 100049, China

4Shanghai Institute of Microsystem and Information Technology,

Chinese Academy of Sciences, ShangHai, 200050, China

5Institute of Modern Physics, Chinese Academy of Sciences, LanZhou, 730000, China

6School of Physics and Astronomy, Sun Yat-Sen University, Guangzhou, 510297, China

The bound beta-decay (BoB) of neutron is also known as the two-body neutron decay, which is a rare decay

mode into a hydrogen atom and an anti-neutrino. The state of neutrino can be exactly inferred by measuring

the state of hydrogen atom, providing a possible pathway to explore new physics. However, this rare decay

mode has not yet been observed so far since it was predicted in 1947. The challenge in observing this decay is

not only that its cross section is extremely low, equivalent to about branching ratio of the order of 10−6of the

three-body decay, but also that the ﬁnal-state hydrogen atom is neutral and has extremely low kinetic energy,

which cannot be effectively detected. In this study, we propose a microcalorimeter-based scheme for measuring

the kinetic energies of hydrogen atoms produced from BoB of ultracold neutrons, which has a great advantage in

terms of accuracy of the energy measurement. In this study, ﬁrst, several important issues that require rigorous

considerations for the decay measurements and possible solutions are discussed. Then, the requirements of the

neutron ﬂux and the appropriate structure design of the microcalorimeter are present by theoretical calculations.

In short, this paper outlines our proposed novel experimental scheme for observing the BoB mode, addressing

the possible solutions to all the necessary problems.

Keywords: Neutron decay, βdecay, Cryogenics detector

I. INTRODUCTION

Fig. 1. Comparison of the two decay modes: 1) a regular three-

body decay mode of the neutron into protons, electrons and neutri-

nos, with the continuum energy spectra for all three; 2) an exotic de-

cay mode of the neutron into a hydrogen atom and an anti-neutrino,

which has a extremely small cross section and the ﬁnal state particles

are both monoenergetic.

Neutron decay is closely related to fundamental physics.

The fact that, no new particles other than the Higgs boson

∗Project supported by the National major scientiﬁc research instrument de-

velopment project (Grant No.11927805)

†Corresponding author, shuozhang@shanghaitech.edu.cn

have been found at the LHC, has prompted a turn to the search

for signatures of new physics in the low and medium-energy

regions [1]. Experiments related to βdecay are an important

avenue to explore the standard model of electroweak interac-

tions, e.g., a neutron decaying into a proton, an electron, and

an electron antineutrino, which is a concise model for study-

ing weak interactions. In 1947 Daudel, Jean and Lecoin [2,3]

have predicted the existence of a two-body β-decay mode

where the daughter nucleus and the electron remain bound. In

the case of the free neutron, the neutron two-body decay mode

is n→H + ¯νe, which is also referred to as ”bound β-decay”

(BoB). As this decay results in a two-body ﬁnal state, it is

theoretically quite straightforward to determine the states of

individual particles. Many theoretical studies have been car-

ried out on this two-body decay [3,4], although it has never

been observed in experiments so far. The successful measure-

ment of this process is of great physical importance [4]. As

the BoB leads to a two-body ﬁnal state, the spin state of the

anti-neutrino is thus mirrored by the outgoing hydrogen atom.

As such, measuring the hyperﬁne spin state of the hydrogen

atom would therefore contain full information relating to the

momentum direction of the antineutrino [5]. Moreover, the

measurement of the BoB branching ratio can also be a solu-

tion to the recently proposed neutron lifetime puzzle [6,8].

The major challenges in observing the BoB decay and in-

vestigating its properties lie in the small predicted branching

ratio ∼4×10−6of the dominated three-body decay mode [7–

9], together with the detection of low-energy electrically neu-

tral hydrogen atoms in the ﬁnal state. According to the theory,

the hydrogen atom in the ﬁnal state has a kinetic energy of

325.7 eV, corresponding to a velocity ∼105m/s, and is ex-

pected to be populated with zero angular momentum, specif-

arXiv:2210.02314v3 [hep-ex] 18 Apr 2023

ically, with 83.2% of atoms in the 1s-state and 10.4% in the

2s-state and the remainder in an ns-state where n≥3[10].

In this study, we propose a scheme to detect the BoB that

will rely on the measurement of H atoms through its energy

spectrum structure, in order to observe for the ﬁrst time this

hitherto unobserved decay mode. As known, the standard

three-body decay mode is n→H++e−+ ¯νe, where the

proton and electron are charged particles that are easily cap-

tured by solid materials, while the antineutrino is extremely

difﬁcult to capture. The total energy in the three-body decay

is conserved, leading to continuum energy spectra for each of

particles. Since the mass of the proton is much larger than

that of the electron and neutrino, the decay energy is obtained

mainly by the electron and neutrino, both of which have ki-

netic energies in the range of 0–782 keV, while the energy

spectrum of the proton lies in the range of 0–750 eV [11].

For the BoB mode, the conservation of momentum and

energy during the decay leads to the energy carried by the

antineutrino is constant, while the kinetic energy of the hy-

drogen atom is also constant (325.7 eV), making it easy to

be captured by solid materials. Since the hydrogen atom in

the ns (≥2) state after the two-body decay can be captured

by the detector, it will de-excite to the 1s state very quickly,

transferring its thermal energy greater than 10.2 eV to the

detector. Thus, the kinetic energy spectra of the hydrogen

atoms on the detector would be a multiple line structure dom-

inated by 325.7 eV and 335.9 eV. The lower right panel of

Fig. 2shows only these two spectral lines, and the other spec-

tral lines from ns states are ignored for the moment. More-

over, three-body-decay protons will introduce a strong back-

ground continuum spectrum contaminating the measurement

of the hydrogen atoms, which needs to be removed to obtain

a high signal-to-noise ratio. Since the charged protons and

electrons are susceptible to an external electric ﬁeld, one can

set up positive and negative electrodes at about 1 kV in a low-

temperature vacuum, resulting in a large difference in signal

amplitudes between electrons with E > 1keV and hydrogen

atoms at 325.7 eV, which therefore can be easily identiﬁed.

In Fig. 3, the expected shapes of energy spectrum before and

after electric ﬁeld screening is shown. As seen, combine with

the 1kV screening electric ﬁeld, the central energy of the elec-

trons is in the energy region of several hundred keV, which is

very different from the line signature of the two-body-decay

hydrogen atoms.

A microcalorimeter is a sensitive detector for heat signals,

with extremely high energy resolution at eV level and no dead

layer, as well as a wide range of available absorption materi-

als [12,13]. The energy of the particle deposition is converted

into heat and the resulting temperature rise is measured. Since

hydrogen atoms, electrons and protons can all generate heat

signals at the detector, and the energy resolution at the eV

level fully satisﬁes the requirement for resolution of a single

energy peak at 325.7 eV, the microcalorimeter detector is thus

an ideal detector for measuring the BoB according to energy

spectrometry. Although electrons and protons below 1 keV

can be completely eliminated by the electric ﬁeld, there are

still some background processes that would produce a con-

tinuum at the detector. As seen from the lower right panel of

Fig. 2, if the initial kinetic energy of neutrons is much less

than 1 eV and the resolution of the detector is around 1 eV,

not only can the hydrogen atom be clearly seen in the 1s or 2s

or even a higher state, but also a high signal-to-background

can be obtained. For the transition edge sensor (TES)-based

microcalorimeter, in the 1 keV energy range, the best reported

energy resolution is about 0.75 eV [14], and the best one we

obtained so far is about 1.4 eV [15], so that the detector per-

formance is basically appropriate for the BoB measurement.

More importantly, as the energy range of interest is around

325.7 eV, a better energy resolution can be obtained by fur-

ther reducing the heat capacity of the microcalorimeter [13].

This paper is organized as follows. In Sect. II, we will

present the theoretical calculations for the BoB and summa-

rize various neutron sources, then discuss the the require-

ments for the BoB measurements, in addition we brieﬂy re-

view the working principle of microcalorimeter. In Sect. III,

we outline our experimental concept and investigate suitable

neutron sources, as well as discuss measurement related is-

sues, such as the 3He problem in refrigerators, the elimination

of proton effects, effects of high-energy particles, the method

of readout electronics, etc. Finally, we draw our summary and

conclusions in Sect. IV.

II. BASIC PRINCIPLES

A. Theoretical Calculations of Neutron Two-Body Decay

Let us consider the BoB process, n→H + ¯νe, where the

expression for the kinetic energy of the hydrogen atom can

be derived from the conservation of energy and momentum.

In the following, the subscripts of n, H, ¯νerepresent neu-

tron, hydrogen atom and electron antineutrino, respectively.

E,Pand Mdenote the energy, the momentum and the rest

mass, respectively. We will use natural units in which c= 1

throughout. First, the conservation of energy leads to

En=EH+E¯νe,(1)

According to the energy–momentum relation and the momen-

tum conservation, PH+P¯νe= 0, Eq. 1is then expressed by

Mn=qM2

H+P2

H+qM2

¯νe+P2

¯νe,(2)

which yields

Mn−qM2

H+P2

H2

=M2

¯νe+P2

H,(3)

and by expanding it, one obtain

n+M2

H−M2

¯νe

2Mn

=qM2

H+P2

H(4)

In the non-relativistic limit for H,

qM2

H+P2

H≈MH+TH,with TH=P2

2MH

(5)

Fig. 2. Comparison of the probability densities of electrons (upper left), neutrinos (upper right) and protons (lower left) produced by neutron

three-body decay and hydrogen atoms (lower right) by two-body decay [11]. The broadening of the hydrogen atom energy spectrum is

determined by the initial kinetic energy of the parent neutron. With varying the initial kinetic energy, the hydrogen atom energy spectra

broadened to 1 eV, 2 eV, 5 eV, and 10 eV are shown. Note that, the predicted probablity density of hydrogen atoms is highly suppressed by

the two-body-decay branching ratio that is assumed to be 4×10−6.

Fig. 3. Same as Fig. 2, but for comparison of the BOB-induced spectral structures before (left) and after (right) electric ﬁeld screening.

Adding a voltage of 1 kV or more can signiﬁcantly eliminate the effects of electrons and protons. The protons can be completely eliminated

and are thus invisible on the plot, since their kinetic energies are less than 1 keV.

Inserting it into Eq. 4, the expression for the kinetic energy of

H, TH, then reads

TH=(Mn−MH)2−M2

¯νe

2Mn

.(6)

As known, Mn−MH≈782.15 keV, Mn= 939.56542 MeV,

and the neutrino energy M¯νe1eV. Based on these values,

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ProposalforMeasurementoftheTwo-bodyNeutronDecayusingMicrocalorimeterShuoZhang,1,yXavierMougeot,2Song-LinWang,3Jian-RongZhou,3Wen-TaoWu,4Jing-KaiXia,1Rui-TianZhang,5andLeZhang61CenterforTransformativeScience,ShanghaiTechUniversity,ShangHai,201210,China2CEA,LIST,LaboratoireNationalHenriBecquerel,CEA-...

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Proposal for Measurement of the Two-body Neutron Decay using Microcalorimeter Shuo Zhang1yXavier Mougeot2Song-Lin Wang3Jian-Rong Zhou3 Wen-Tao Wu4Jing-Kai Xia1Rui-Tian Zhang5and Le Zhang6

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