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Review on Proton Radioactivity in the Actinide Region: Experimental
status, Theoretical Approaches and Future perspectives
M. G. Srinivas*
Department of Physics, Government College for Women, Kolar-563101, Karnataka, India
DOI: https://doi.org/10.51583/IJLTEMAS.2026.150600136
Received: 01 July 2026; Accepted: 07 July 2026; Published: 17 July 2026
ABSTRACT
Proton radioactivity is one of the most distinctive manifestations of quantum tunnelling in atomic nuclei and
provides a powerful probe of nuclear structure beyond the proton drip line. Since its theoretical prediction by
Goldanskii in 1960 and subsequent experimental confirmation, proton emission has become an important
spectroscopic tool for investigating single-particle configurations, shell evolution, nuclear deformation, and the
interplay between nuclear and Coulomb interactions in proton-rich systems. While proton radioactivity has been
extensively studied in light, medium-mass, and rare-earth nuclei, comparatively little attention has been devoted
to the actinide region despite its unique structural and decay properties.This review presents a comprehensive
overview of proton radioactivity in actinide nuclei (89 ≤ Z ≤ 103), with emphasis on recent theoretical
developments and future experimental prospects. The historical evolution of the field, experimental status,
theoretical models, and decay systematics are critically discussed. Particular attention is given to the prediction
of proton-emitting actinides, the influence of proton-decay energy and quantum tunnelling on half-lives, Geiger–
Nuttall-type correlations, and the competition between proton emission, α decay, β decay, spontaneous fission,
and cluster radioactivity. The predictive performance of widely used theoretical approaches, including the
Coulomb and Proximity Potential Model (CPPM), Generalized Liquid Drop Model (GLDM), Effective Liquid
Drop Model (ELDM), Density-Dependent Michigan 3-Yukawa (DDM3Y) interaction, Jeukenne–Lejeune–
Mahaux (JLM) interaction, and related microscopic models, is also evaluated.The review highlights the most
promising candidate proton emitters in the actinide region and discusses the prospects for their experimental
observation using next-generation rare-isotope facilities. By integrating current theoretical predictions with
available experimental knowledge, this article provides a comprehensive assessment of proton radioactivity in
heavy nuclei and underscores its importance for understanding the limits of nuclear stability and the structure of
proton-rich actinides.
Keywords: Proton radioactivity; Actinides; Proton drip line; Quantum tunneling; Nuclear structure
INTRODUCTION
The study of radioactive decay has been fundamental to the development of nuclear physics and continues to
provide valuable insights into the structure and stability of atomic nuclei. In addition to the well-known decay
modes such as alpha decay, beta decay, and spontaneous fission, the exploration of nuclei far from the valley of
stability has revealed several exotic decay processes. Among these, proton radioactivity occupies a special place
because it occurs in nuclei beyond the proton drip line, where the nuclear binding is insufficient to prevent the
escape of a proton. The concept of proton radioactivity was first introduced by Goldanskii in 1960, who predicted
that proton-rich nuclei could undergo one-proton and two-proton emission. Experimental confirmation followed
a decade later with the observation of proton emission from the isomeric state of
53
Co. A major breakthrough
came in 1982 with the discovery of ground-state proton radioactivity in
151
Lu, which established proton emission
as a distinct radioactive decay mode and stimulated extensive experimental and theoretical investigations. Since
then, proton radioactivity has been observed in numerous nuclei ranging from iodine to bismuth, providing a
unique opportunity to probe nuclear properties at the limits of stability.
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Unlike conventional decay processes, proton emission is governed by quantum tunneling through the combined
Coulomb and centrifugal barriers surrounding the nucleus. As a result, proton-decay half-lives are highly
sensitive to the decay energy, angular momentum transfer, nuclear deformation, shell structure, and
spectroscopic factors. This sensitivity makes proton radioactivity an exceptionally powerful tool for studying
single-particle states and testing nuclear models in proton-rich systems. While proton radioactivity has been
extensively explored in light, medium-mass, and rare-earth nuclei, comparatively little attention has been
devoted to the actinide region. The actinides (89 ≤ Z ≤ 103) constitute a particularly challenging domain because
of their large proton numbers, strong Coulomb repulsion, pronounced quadrupole and octupole deformations,
and the presence of competing decay modes such as alpha decay and spontaneous fission. These factors
significantly influence the probability of proton emission and complicate both experimental detection and
theoretical interpretation.
Recent advances in theoretical modeling have renewed interest in proton radioactivity in actinide nuclei.
Systematic studies employing the Coulomb and Proximity Potential Model (CPPM), Generalized Liquid Drop
Model (GLDM), Effective Liquid Drop Model (ELDM), density-dependent interactions, and microscopic
approaches have predicted several neutron-deficient actinides that may exhibit measurable proton-decay half-
lives. These investigations suggest that proton emission can become a competitive decay mode in selected nuclei
near the proton drip line, thereby extending the known region of proton radioactivity into heavier nuclear
systems. Understanding proton radioactivity in actinides is important not only for defining the limits of nuclear
stability but also for improving our knowledge of shell effects, deformation, and tunneling phenomena in
strongly charged nuclei.
The present review aims to summarize the current status of proton radioactivity in actinide nuclei. Historical
developments, experimental progress, theoretical approaches, decay systematics, and the competition between
proton emission and other decay modes are discussed. Particular emphasis is placed on predicted actinide proton
emitters, the role of nuclear structure and deformation, and the comparative performance of various theoretical
models. Finally, future prospects for experimental discovery and theoretical refinement are outlined, highlighting
the continuing importance of proton radioactivity in understanding the boundaries of nuclear existence.
Historical Timeline of Proton Radioactivity
Proton radioactivity originated with the pioneering work of Goldanskii, who first predicted the possibility of
one-proton and two-proton radioactivity in proton-rich nuclei located beyond the proton drip line [1]. This
prediction was experimentally confirmed a decade later when Jackson et al. observed proton emission from the
isomeric state of
53m
Co, providing the first direct evidence of proton radioactivity [2].A major breakthrough
occurred in 1982 with the discovery of ground-state proton radioactivity in
151
Lu by Hofmann et al. [3]. Shortly
thereafter, Klepper et al. reported proton emission from
157
Ta, confirming that proton radioactivity is a general
phenomenon among nuclei beyond the proton drip line [4]. The subsequent identification of numerous proton
emitters in the rare-earth region during the 1980s and 1990s significantly expanded the known proton-emitting
landscape. As summarized by Woods and Davids, proton radioactivity became an important spectroscopic tool
for studying single-particle orbitals, angular momentum effects, and nuclear deformation in proton-rich nuclei
[5]. The timeline further highlights the emergence of modern theoretical descriptions of proton emission. During
the late 1990s, Maglione, Ferreira, and Liotta demonstrated that proton-decay probabilities are strongly
influenced by nuclear deformation and shell structure [27]. Their subsequent comprehensive review established
the importance of spectroscopic factors, Nilsson orbitals, and microscopic structure effects in determining
proton-decay half-lives [28]. Another major milestone is the discovery of two-proton radioactivity. The first
evidence for this exotic decay mode was reported by Pfützner et al. in
45
Fe [10], followed by the first direct
observation by Blank et al. [9]. The development of comprehensive theoretical frameworks culminated in the
work of Delion, Liotta, and Wyss, who provided a unified description of proton radioactivity and its connection
to nuclear structure and spectroscopic factors [48]. The most recent milestone represented in the timeline is the
extension of proton-radioactivity investigations into the actinide region. Systematic studies by Srinivas et al.
predicted numerous proton-unstable actinides and demonstrated that proton emission may compete with α decay
in selected neutron-deficient nuclei [35,36]. These investigations revealed Geiger–Nuttall-type behavior in
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heavy nuclei and identified several promising candidates for future experimental observation, thereby extending
proton-radioactivity research into one of the heaviest regions of the nuclear chart.
Theoretical Description of Proton Emission
Proton radioactivity is treated as a quantum tunneling process through a potential barrier composed of
Coulomb, nuclear and centrifugal components [50].
The half-life is expressed as
=

where λ = is the decay constant
ν being the assault frequency and P the barrier penetrability [51].
The penetrability is usually calculated using the WKB approximation [50,51]:
P=exp[−
󰇛 󰇜


dr].
The Coulomb and Proximity Potential Model (CPPM) has been widely applied to alpha decay, cluster
radioactivity and proton emission [25,26,37].
In this approach, V(r) = V
C
(r) + V
P
(r) + V
ℓ
(r)
Where V
C
, V
P
and V
ℓ
denote Coulomb, proximity and centrifugal potentials respectively.
Proton Radioactivity in the Actinide Region
The actinide region extends from Ac (Z = 89) to Lr (Z = 103). Systematic investigations of proton decay in
actinides have been carried out using CPPM and related approaches [35,36]. The listed nuclei satisfy the
condition Q
p
>0. These studies demonstrated that proton emission is energetically allowed in several neutron-
deficient isotopes of Ac, Pa, U, Np, Pu, Am, Cm and neighboring elements. The first dedicated investigation
of proton decay in actinides employed the Coulomb and Proximity Potential Model and compared proton
half-lives with alpha decay, beta decay and spontaneous fission half-lives [35]. The study identified
numerous candidate proton emitters and showed that proton emission may act as a competing decay mode
in nuclei near the proton drip line. Subsequently, systematic studies of actinides confirmed the existence of
Geiger–Nuttall-type behavior for proton emission and highlighted possible proton emitters with proton-
decay half-lives that may be accessible to future experimental investigations [36].
The nuclei listed in Table 1 represent the currently predicted proton emitters in the actinide region (89 ≤ Z
≤ 103) identified through systematic calculations using the Coulomb and Proximity Potential Model (CPPM)
and related theoretical approaches [35,36]. A total of approximately seventy-five proton-unstable isotopes
are predicted across the actinide region. The largest concentrations of predicted proton emitters occur in the
actinium, protactinium, neptunium, americium, berkelium, and mendelevium isotopic chains, indicating
broad regions of proton instability among neutron-deficient actinides [35].
Among the lighter actinides, the actinium and protactinium isotopes exhibit particularly extensive proton-
emitting sequences. Thirteen proton-unstable isotopes are predicted for actinium and twelve for
protactinium, suggesting that these nuclei lie closest to the proton drip line within the actinide region. Their
relatively large proton-decay energies and favorable tunneling probabilities make them attractive candidates
for future experimental investigations. Similarly, the neptunium and americium chains contain a significant
number of predicted proton emitters, reflecting the persistence of proton instability over a wide range of
neutron numbers [35,36].
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The results also reveal a strong dependence of proton stability on nuclear shell structure and deformation.
Certain elements, such as thorium, uranium, plutonium, curium, and californium, contain only a small
number of predicted proton emitters, whereas no energetically favorable proton-emitting isotope is identified
for fermium. The absence of energetically favorable proton emitters in the fermium isotopic chain is also
noteworthy. This result suggests the presence of enhanced nuclear stability in this region and highlights the
influence of shell effects on proton separation energies. Similar structural effects are known to play an
important role in determining the stability of heavy and super heavy nuclei.
Overall, the distribution of predicted proton emitters presented in Table 1 indicates that proton radioactivity
may occur over a much broader region of the actinide chart than previously recognized. These nuclei provide
important targets for future experimental searches and serve as a valuable testing ground for theoretical
models of charged-particle emission. Experimental confirmation of even a small fraction of these predicted
proton emitters would significantly improve our understanding of proton-rich nuclear matter and help define
the limits of nuclear stability in the heaviest known elements [35,36].
Table 1. Predicted Proton Emitters in the Actinide Region (89 ≤ Z ≤ 103) [35,36]
Element
Predicted Proton Emitters
Ac (Z=89)
195
Ac,
196
Ac,
197
Ac,
198
Ac,
199
Ac,
200
Ac,
201
Ac,
202
Ac,
203
Ac,
204
Ac,
205
Ac,
206
Ac,
207
Ac
Th (Z=90)
198
Th,
199
Th
Pa (Z=91)
200
Pa,
201
Pa,
202
Pa,
203
Pa,
204
Pa,
205
Pa,
206
Pa,
207
Pa,
208
Pa,
209
Pa,
212
Pa,
213
Pa
U (Z=92)
203
U
Np (Z=93)
206
Np,
207
Np,
208
Np,
209
Np,
210
Np,
211
Np,
212
Np,
213
Np,
214
Np,
215
Np,
216
Np,
217
Np
Pu (Z=94)
209
Pu
Am (Z=95)
212
Am,
213
Am,
214
Am,
215
Am,
216
Am,
217
Am,
218
Am,
219
Am,
220
Am,
224
Am
Cm (Z=96)
215
Cm
Bk (Z=97)
218
Bk,
219
Bk,
220
Bk,
221
Bk,
222
Bk,
223
Bk,
224
Bk,
225
Bk,
226
Bk,
227
Bk
Cf (Z=98)
221
Cf
Es (Z=99)
224
Es,
225
Es,
226
Es,
227
Es,
228
Es,
229
Es,
230
Es,
231
Es
Fm (Z=100)
No energetically favorable proton emitter identified
Md (Z=101)
229
Md,
230
Md,
231
Md,
232
Md,
233
Md,
234
Md,
235
Md,
236
Md,
237
Md,
238
Md,
239
Md
No (Z=102)
232
No,
233
No
Lr (Z=103)
235
Lr,
236
Lr,
237
Lr,
238
Lr,
239
Lr,
240
Lr,
241
Lr,
242
Lr,
243
Lr
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Table 2. Proton decay half-lives, penetration factors, and energy released for selected actinide nuclei
predicted to undergo proton radioactivity in the Actinide Region [36]
Nucleus
Q-value (MeV)
Half-life, T₁/₂ (s)
¹⁹⁵Ac
2.161
1.892 × 10⁻⁷
²⁰⁰Pa
2.111
1.073 × 10⁻⁶
²⁰⁶Np
1.911
7.471 × 10⁻⁵
²¹²Am
2.051
2.267 × 10⁻⁵
²¹⁸Bk
2.241
4.142 × 10⁻⁶
²²⁴Es
2.181
2.976 × 10⁻⁵
²²⁹Md
2.251
2.883 × 10⁻⁵
²³⁵Lr
2.161
3.273 × 10⁻⁴
The results presented in Table 2 provide valuable insight into the stability of neutron-deficient actinide
nuclei located beyond the proton drip line. All the nuclei considered possess positive Q-values, ranging from
1.911 to 2.251 MeV, confirming that proton emission is energetically possible. These decay energies are
sufficiently large to reduce the effective potential barrier and enhance the probability of proton tunnelling
through the combined Coulomb and centrifugal barriers, making proton radioactivity a viable decay mode
in these heavy nuclei [36].
A strong dependence of the proton-decay half-life on the decay energy is evident from the calculated results.
As expected from quantum tunnelling theory, an increase in Q-value leads to a higher barrier penetration
probability and, consequently, a shorter proton-decay half-life. This trend is clearly illustrated by nuclei such
as ¹⁹⁵Ac, ²⁰⁰Pa, and ²¹⁸Bk, which exhibit relatively large penetration factors and correspondingly short half-
lives on the order of 10⁻⁷–10⁻⁶ S. In particular, ¹⁹⁵Ac having a comparatively high proton-decay energy with
the shortest calculated half-life, suggests that it may be one of the most promising proton emitters in the
actinide region [36].In contrast, nuclei such as ²⁰⁶Np and ²³⁵Lr exhibit lower penetration probabilities,
resulting in longer proton-decay half-lives..
The results presented in Table 2 also provide an important assessment of the predictive capability of the
Coulomb and Proximity Potential Model (CPPM). By incorporating the Coulomb interaction, nuclear
proximity potential, and centrifugal contribution within the WKB approximation, the model successfully
reproduces the conditions required for proton emission in heavy nuclei and predicts a number of
energetically favorable proton emitters in the actinide region. These calculations further demonstrate that
CPPM remains a robust theoretical framework for describing charged-particle emission from highly
deformed and strongly Coulomb-repulsive nuclear systems [35,36].
Overall, the calculated decay characteristics indicate that proton radioactivity is a realistic and potentially
observable decay mode for several neutron-deficient actinide isotopes. The predicted half-lives, together
with the favorable proton-decay energies, suggest that nuclei such as ¹⁹⁵Ac, ²⁰⁰Pa, ²¹²Am, and ²¹⁸Bk deserve
high priority in future experimental campaigns. Confirmation of proton emission from these nuclei would
not only extend the presently known limits of proton radioactivity into the actinide region but also provide
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stringent tests of quantum-tunnelling models, improve our understanding of proton-rich heavy nuclei, and
help define the proton drip line for the heaviest elements [35,36].
FIGURE 1: Nuclear Chart of The Actinide Region (89 ≤ Z ≤ 103) Showing The Estimated Proton Drip
Line And The Predicted Proton-Emitting Nuclei Identified In Systematic Proton-Decay Studies. The
Highlighted Nuclei (
195
ac,
200
pa,
206
np,
212
am,
218
bk,
224
es,
229
md And
235
lr) Exhibit Positive Proton-
Decay Energies And Calculated Half-Lives Favorable For Proton Emission.[35,36,37,40]
Figure 2. Variation of proton-decay energy (Qp) with mass number (A) for selected actinide isotopic chains
(Ac, Pa, Np, Am, Bk, Es, Md, and Lr). The proton-decay energy generally decreases with increasing mass
number, indicating movement away from the proton drip line and a corresponding reduction in proton-
emission probability. [36] The trend is consistent with modern microscopic descriptions of proton
radioactivity and nuclear-structure effects in heavy nuclei [27,28,48].
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Figure 3. Variation of logarithmic proton-decay half-lives, log
10
(T1/2)with mass number (A) for selected
actinide isotopic chains (Ac, Pa, Np, Am, Bk, Es, Md, and Lr). The proton-decay half-lives generally
increase with increasing mass number, reflecting the reduction in proton-decay energy and barrier
penetrability as nuclei move away from the proton drip line. [27,28,36,48].
Experimental Status
The experimentally confirmed proton emitters summarized in Table 3 constitute the cornerstone of
proton-radioactivity research and provide the primary experimental evidence for proton emission as a
distinct radioactive decay mode. These nuclei extend from iodine (Z = 53) to bismuth (Z = 83). Their
measured proton-decay energies, typically between 0.8 and 1.8 MeV, are accompanied by half-lives
spanning several orders of magnitude. This broad variation reflects the exponential dependence of proton-
decay probability on the barrier penetration process and illustrates the remarkable sensitivity of proton
emission to relatively small changes in decay energy [5].
The rare-earth proton emitters have played a particularly significant role in advancing the understanding
of proton radioactivity. Nuclei such as ¹³¹Eu, ¹⁴¹Ho, ¹⁴⁵Tm, ¹⁴⁷Tm, ¹⁵⁰Lu, and ¹⁵¹Lu have served as
benchmark systems for investigating the interplay between nuclear structure and quantum tunnelling.
Experimental studies of these isotopes demonstrated that proton-decay properties are strongly influenced
by nuclear deformation, angular-momentum transfer, and the underlying single-particle configurations.
In particular, proton emission from ¹⁴¹Ho provided compelling evidence for the role of nuclear
deformation in modifying decay probabilities, while investigations of ¹⁵⁰Lu and ¹⁵¹Lu revealed proton-
decay fine structure, offering direct spectroscopic information on the daughter nuclei and reinforcing the
value of proton radioactivity as a sensitive probe of nuclear structure [5–7].
Table 3. Experimentally Established Proton Emitters and Landmark Two-Proton Emitters
Nucleus
Z
Decay
Mode
Q
p
/ Q
2p
(MeV)
log
10
T
1/2
(S)
Key Observation
Reference
¹⁰⁹I
53
1p
0.829
−3.99
One of the first identified proton emitters
[5]
¹¹³Cs
55
1p
0.978
−4.78
Ground-state proton emitter
[5]
¹¹⁷La
57
1p
0.806
−1.87
Proton emission near drip line
[5]
¹³¹Eu
63
1p
0.932
−0.82
Rare-earth proton emitter
[5]
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¹⁴¹Ho
67
1p
1.17
−2.39
Direct observation of proton radioactivity
[6]
¹⁴⁵Tm
69
1p
1.75
−5.41
Deformed proton emitter
[5]
¹⁴⁷Tm
69
1p
1.07
−0.59
Ground-state proton radioactivity
[5]
¹⁵⁰Lu
71
1p
1.28
−1.18
Proton decay fine structure
[7]
¹⁵¹Lu
71
1p
1.26
−0.82
First well-established ground-state proton
emitter
[7]
¹⁵⁵Ta
73
1p
1.79
−2.49
Proton emission near drip line
[8]
¹⁵⁷Ta
73
1p
0.95
−0.52
Low-angular-momentum proton emitter
[8]
¹⁶¹Re
75
1p
1.21
−3.43
Heavy proton emitter
[5]
¹⁶⁷Ir
77
1p
1.09
−3.96
Proton-rich odd-Z nucleus
[5]
¹⁷¹Au
79
1p
1.47
−4.77
Heavy proton emitter
[5]
¹⁷⁷Tl
81
1p
1.18
−1.17
Near-lead proton emitter
[5]
¹⁸⁵Bi
83
1p
1.62
−4.23
Heaviest established proton emitter
[5]
⁴⁵Fe
26
2p
1.15–1.20
−2.4
First evidence for two-proton
radioactivity
[10]
⁴⁵Fe
26
2p
1.15–1.20
−2.4
First direct observation of two-proton
radioactivity
[9]
The experimentally known proton-emitting region extends further toward heavier nuclei, including ¹⁵⁵Ta, ¹⁶¹Re,
¹⁶⁷Ir, ¹⁷¹Au, ¹⁷⁷Tl, and ¹⁸⁵Bi. Their measured decay energies and half-lives have been widely used to assess the
predictive accuracy of various theoretical approaches, including the Coulomb and Proximity Potential Model
(CPPM), the Generalized Liquid Drop Model (GLDM), the Effective Liquid Drop Model (ELDM), the Density-
Dependent M3Y (DDM3Y) interaction, and the Jeukenne–Lejeune–Mahaux (JLM) microscopic model. The
ability of these models to reproduce the observed decay properties has significantly improved confidence in their
application to proton-rich nuclei beyond the range of current experimental data [5,8].
Table 3 also illustrates an important milestone in the evolution of charged-particle radioactivity through the
discovery of two-proton (2p) emission. The observation of this decay mode in ⁴⁵Fe, first reported
experimentally by Pfützner et al. [10] and subsequently confirmed by Blank et al. [9], established two-proton
radioactivity as a genuine three-body decay process. Collectively, the experimentally established proton emitters
listed in Table 3 provide the benchmark database against which theoretical models of proton radioactivity are
evaluated. Their accurately measured proton-decay energies, branching ratios, and half-lives have been
instrumental in refining theoretical descriptions of quantum tunnelling and nuclear structure. Furthermore, these
experimental results serve as a reliable foundation for predicting proton emission in unexplored regions of the
nuclear landscape, including the neutron-deficient actinide and superheavy nuclei discussed later in this review
[5,9,10].
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Competition Between Decay Modes
The competition among proton decay, α decay, and spontaneous fission represents one of the defining features
of radioactive decay in proton-rich actinide nuclei. Owing to their large proton numbers and complex nuclear
structures, these nuclei can decay through multiple channels, with the dominant mode determined by the
interplay between decay energy, quantum tunnelling probability, shell structure, deformation, and fission
stability. The calculated half-lives presented in Table 4 provide a systematic comparison of these competing
decay processes and illustrate how the preferred decay mode evolves across the actinide region [35,36].
For the lighter neutron-deficient actinides, including ¹⁹⁵Ac, ²⁰⁰Pa, ²⁰⁶Np, ²¹²Am, and ²¹⁸Bk, proton emission is
predicted to be the dominant decay mechanism. These nuclei exhibit negative values of log
10
T
1/2
,p (S)
corresponding to proton-decay half-lives in the sub-microsecond to microsecond range. In contrast, both α-decay
and spontaneous-fission half-lives are considerably longer, indicating that proton emission is the most probable
decay channel. Their relatively high proton-decay energies (Qp ≈ 1.9–2.3 MeV) substantially increase the barrier
transmission probability, resulting in rapid proton emission through quantum tunnelling. Consequently, these
isotopes are expected to be among the most promising candidates for future experimental observation of proton
radioactivity in the actinide region [35,36].
Table 4. Competition Between Proton Decay, α Decay, and Spontaneous Fission in Selected Actinide
Proton Emitters
Nucleus
Q
p
(MeV)
log
10
T
1/2
,p (S)
log
10
T
1/2
,α (S)
log
10
T
1/2,SF
(S)
Dominant Decay Mode
Reference
¹⁹⁵Ac
2.161
−6.7230
1.9019
19.2850
Proton decay
[35,36]
²⁰⁰Pa
2.111
−5.9691
2.9029
12.2615
Proton decay
[35,36]
²⁰⁶Np
1.911
−4.1216
4.5136
6.7169
Proton decay
[35,36]
²¹²Am
2.051
−4.6445
4.7376
1.6163
Proton decay
[35,36]
²¹⁸Bk
2.241
−5.3828
4.7539
-3.0072
Proton decay
[35,36]
²²⁴Es
2.181
−4.5262
5.7952
-7.1242
Spontaneous fission
[35,36]
²²⁹Md
2.251
−4.5400
6.3166
-11.0676
Spontaneous fission
[35,36]
²³⁵Lr
2.161
−3.4850
7.5036
-14.0132
Spontaneous fission
[35,36]
A marked change in decay behavior is observed as the atomic number increases. For heavier nuclei such as ²²⁴Es,
²²⁹Md, and ²³⁵Lr, spontaneous fission becomes increasingly competitive and eventually surpasses both proton
and α decay. The calculated spontaneous-fission half-lives decrease significantly with increasing nuclear charge,
reflecting the growing influence of Coulomb repulsion and the progressive reduction of the fission barrier in
very heavy nuclei. Although proton emission remains energetically allowed, the overwhelming probability of
spontaneous fission effectively suppresses proton radioactivity in these isotopes. This transition highlights the
increasing instability of the heaviest actinides against nuclear fission and defines an upper limit for the
occurrence of observable proton emission [35].
The calculated α-decay half-lives exhibit a more gradual increase across the sequence from actinium to
lawrencium. While α decay remains an important competing process throughout the region, it is generally less
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favorable than proton emission in the lighter proton-rich isotopes and becomes subordinate to spontaneous
fission in the heaviest nuclei. These results emphasize that no single decay mode dominates the entire actinide
region. The systematic trends summarized in Table 4 reveal a clear evolution of radioactive decay with increasing
atomic number. Proton emission predominates in lighter actinides situated close to the proton drip line, where
positive proton-decay energies and relatively low potential barriers favor rapid quantum tunnelling. Overall, the
calculated results demonstrate that proton radioactivity is a realistic and potentially observable decay mode for
several neutron-deficient actinide isotopes, particularly in the lighter members of the series. At the same time,
the rapid increase in spontaneous-fission probability toward the heaviest actinides imposes a natural boundary
on the proton-emitting region. These findings not only identify the most promising candidates for future
experimental investigation but also provide stringent tests for theoretical models describing charged-particle
emission, quantum tunnelling, and nuclear stability at the limits of the nuclear landscape [35,36]
Figure 4. Competition between proton (p), α, β, and spontaneous-fission (SF) decay modes in proton-rich
actinide isotopic chains. The figure illustrates the relative importance of the competing decay channels as a
function of mass number. Proton emission is favored near the proton drip line, whereas α decay dominates most
actinide nuclei. With increasing atomic and mass number, spontaneous fission becomes progressively more
important and eventually dominates in the heaviest actinides. The figure is reconstructed from systematic
calculations of proton decay, α decay, and spontaneous-fission half-lives reported in Refs. [35,36] and with the
general theoretical understanding of charged-particle emission in heavy nuclei [5,27,28,48].
7.Geiger–Nuttall Systematics in Actinide Proton Emitters
One of the most important characteristics of proton radioactivity is its systematic relationship between decay
energy and half-life, which closely resembles the well-established Geiger–Nuttall law for α decay. In analogy
with α emission, the proton-decay half-life can be expressed in the form
log
10
T
1/2
= a.
+ b , where Q
p
is the proton-decay energy and (a) and (b) are constants determined from
experimental or theoretical systematics.
Table 5. Geiger–Nuttall-Type Systematics of Proton Radioactivity in Actinide Nuclei
Actinide Series
Predicted Proto
Emitters
Observed Trend of log
10
(T
1/2
)
vs Z
d
Q
p
−1/2
Geiger–Nuttall
Behaviour
Reference
Ac (Z=89)
195–207
Ac
Strong linear increase of log
10
(T
1/2
)
with Z
d
Q
p
−1/2
Confirmed
[36]
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Th (Z=90)
198–199
Th
Linear correlation observed
Confirmed
[36]
Pa (Z=91)
200–209
Pa,
212–213
Pa
Nearly linear dependence
Confirmed
[36]
U (Z=92)
203
U
Consistent with global trend
Confirmed
[36]
Np (Z=93)
206–217
Np
Linear behaviour over predicted
emitters
Confirmed
[36]
Pu (Z=94)
209
Pu
Follows expected trend
Confirmed
[36]
Am (Z=95)
212–224
Am
Approximately linear relation
Confirmed
[36]
Cm (Z=96)
215
Cm
Linear behaviour observed
Confirmed
[36]
Bk (Z=97)
218–227
Bk
Good linear correlation
Confirmed
[36]
Cf (Z=98)
221
Cf
Consistent trend
Confirmed
[36]
Es (Z=99)
224–231
Es
Linear increase of half-life with
decreasing Q
p
Confirmed
[36]
Md(Z=101)
229–239
Md
Strong Geiger–Nuttall-type behaviour
Confirmed
[36]
No (Z=102)
232–233
No
Limited data but consistent
Confirmed
[36]
Lr (Z=103)
235–243
Lr
Linear correlation maintained
Confirmed
[36]
The calculated results presented in Table 6 reveal that proton-emitting actinide nuclei exhibit an approximately
linear dependence of the logarithmic half-life on Z
d
Q
p
−1/2
, where (Z
d
) denotes the charge of the daughter nucleus.
Such linear behavior has been demonstrated for neutron-deficient actinides using the Coulomb and Proximity
Potential Model (CPPM) and is consistent with systematic studies of proton emitters throughout the nuclear chart
[36]. Similar Geiger–Nuttall-type relationships have also been reported by Delion et al. [27,48] and Qi et al.
[28], confirming the universality of this trend across different mass regions.
The isotopic chains of actinium, protactinium, neptunium, americium, berkelium, einsteinium, mendelevium,
and lawrencium all display nearly linear systematics. This observation indicates that proton emission in heavy
nuclei is governed by the same fundamental tunnelling mechanism that successfully explains proton radioactivity
in lighter rare-earth nuclei
From a practical perspective, the systematics summarized in Table 6 provide an important predictive tool for
identifying new proton emitters near the proton drip line. Once the proton-decay energy is estimated, the
corresponding half-life can be obtained with reasonable accuracy from the linear relationship, even for nuclei
that have not yet been produced experimentally. Consequently, Geiger–Nuttall-type correlations serve not only
as a powerful test of theoretical models but also as a valuable guide for future experimental programs aimed at
discovering proton radioactivity in the actinide and super heavy regions.
Overall, the observed linear dependence between proton-decay half-life and Z
d
Q
p
−1/2
reinforces the interpretation
of proton radioactivity as a barrier-penetration phenomenon analogous to α decay. The consistency of these
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systematics across a wide range of actinide isotopes provides strong support for the theoretical description of
proton emission and further strengthens confidence in predictions of yet-unobserved proton-rich nuclei beyond
the currently known limits of nuclear stability [27,28,36,48].
Figure 5. Geiger–Nuttall-type systematics for proton radioactivity in actinide isotopic chains. The logarithmic
proton-decay half-lives, log
10
(T
1/2
), are plotted as a function of Z
d
Q
p
−1/2,
where Z
d
is the proton number of the
daughter nucleus and Q
p
is the proton-decay energy. The approximately linear behavior observed for the Ac, Pa,
Np, Am, Bk, Es, Md, and Lr isotopic chains confirms that proton emission in actinides follows a Geiger–Nuttall-
type relationship analogous to that observed in α decay. [35,36].
Future Experimental Prospects
Although theoretical studies have considerably advanced our understanding of proton radioactivity in the
actinide region, experimental evidence remains scarce. The production of proton-rich actinides is inherently
difficult because of their extremely low formation cross-sections, short lifetimes, and the strong competition
from α decay and spontaneous fission. These factors have limited the direct observation of proton emission in
heavy nuclei. Nevertheless, rapid progress in radioactive-ion-beam technology, recoil-separation techniques, and
high-resolution detector systems has created new opportunities to explore this largely uncharted region of the
nuclear landscape [5,8,11].
The emergence of next-generation rare-isotope facilities is expected to transform experimental investigations of
proton-rich heavy nuclei. The Facility for Rare Isotope Beams (FRIB) in the United States provides high-
intensity primary beams and advanced isotope-production capabilities, enabling access to increasingly exotic
nuclei near the proton drip line. Likewise, the Facility for Antiproton and Ion Research (FAIR) in Germany will
support precision studies of heavy and superheavy nuclei through intense heavy-ion beams, efficient recoil
separators, and advanced spectroscopic instrumentation. Complementary capabilities at the Radioactive Isotope
Beam Factory (RIBF) in Japan and the Grand Accélérateur National d’Ions Lourds (GANIL) in France are also
expected to play an important role in extending proton-radioactivity studies toward neutron-deficient actinides
and neighboring heavy elements [11,66].
A primary objective of future experimental programs is the verification of theoretically predicted proton-emitting
actinides. Calculations based on the Coulomb and Proximity Potential Model (CPPM), the Generalized Liquid
Drop Model (GLDM), the Effective Liquid Drop Model (ELDM), and several microscopic approaches
consistently predict a number of proton-unbound isotopes extending from actinium to lawrencium [35,36].
Experimental confirmation of even a few of these candidates would provide stringent tests of existing proton-
decay models, improve our knowledge of the proton drip line in heavy nuclei, and establish new benchmarks for
theoretical calculations.
Another major research direction involves precise measurements of branching ratios among competing decay
modes. In proton-rich actinides, proton emission often competes directly with α decay and spontaneous fission,
and the relative probabilities of these processes are highly sensitive to nuclear structure and barrier
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characteristics. Accurate branching-ratio measurements would therefore provide valuable information on
tunnelling probabilities, decay dynamics, deformation effects, and shell structure, enabling more rigorous
validation of theoretical descriptions of charged-particle emission [35,36,48,69].
Future experiments are also expected to focus on determining spectroscopic factors, which quantify the overlap
between the wave functions of the parent and daughter nuclei. Because proton emission is strongly influenced
by the underlying single-particle configuration, spectroscopic factors provide direct insight into orbital
occupancies, shell evolution, and deformation effects in proton-rich nuclei. Comparisons between
experimentally extracted spectroscopic factors and theoretical predictions will continue to play a crucial role in
refining nuclear-structure models and improving the predictive accuracy of proton-decay calculations [5,48].
The search for two-proton (2p) radioactivity in heavier systems represents another exciting frontier. Since the
first observation of two-proton decay in ⁴⁵Fe and its subsequent confirmation [9,10], interest in correlated proton
emission has grown considerably. Although all experimentally established two-proton emitters are currently
confined to lighter mass regions, theoretical studies suggest that suitable conditions for simultaneous multi-
proton emission may also exist in selected proton-rich heavy nuclei. Verification of such decay modes would
provide unique information on proton–proton correlations, pairing interactions, and three-body decay dynamics,
thereby extending the present understanding of exotic radioactive decay [10,15,57–59].
Looking beyond the actinides, theoretical calculations indicate that proton radioactivity may also become
relevant in selected super heavy nuclei located near the proton drip line [67,68]. Observation of proton emission
in this region would offer valuable insight into shell stabilization, deformation, and the persistence of quantum
shell effects in nuclei approaching the predicted island of stability. Such measurements would represent a major
advance in heavy-element physics and provide an important test of modern nuclear-structure theories [46].
Continued improvements in experimental instrumentation will be equally important for achieving these
objectives. The development of high-granularity double-sided silicon strip detectors, digital data-acquisition
systems, efficient recoil separators, and position-sensitive detector arrays has significantly increased the
sensitivity for detecting rare decay events. These technologies enable more precise measurements of decay
energies, half-lives, branching ratios, and angular correlations, thereby improving the reliability of proton-
radioactivity studies in nuclei produced with extremely low yields [5,11].
In summary, the combined progress in radioactive-ion-beam facilities, detector technology, and theoretical
modelling is expected to open a new era in the study of proton radioactivity in heavy nuclei. Experimental
verification of predicted proton-emitting actinides, detailed investigations of competing decay modes, and the
possible discovery of heavy two-proton emitters will substantially enhance our understanding of nuclear
structure, quantum tunnelling, and the limits of nuclear stability. These efforts will not only test existing
theoretical frameworks but also provide essential guidance for future exploration of the actinide and super heavy
regions of the nuclear chart [35,36].
Future Perspectives
The rapid advancement of rare-isotope accelerator facilities is expected to greatly expand experimental access
to proton-rich actinide nuclei that have so far remained beyond the reach of conventional production techniques.
Modern facilities such as the Facility for Rare Isotope Beams (FRIB, USA), the Facility for Antiproton and Ion
Research (FAIR, Germany), the Radioactive Isotope Beam Factory (RIKEN, Japan), and the Grand Accélérateur
National d’Ions Lourds (GANIL, France) combine high-intensity ion beams with advanced isotope-separation
and decay-spectroscopy systems, making them well suited for exploring nuclei located close to the proton drip
line [17,40]. Experimental identification of new proton emitters in the actinide region would provide valuable
information on shell evolution, nuclear deformation, and the limits of stability in heavy proton-rich systems.
The nuclei listed in Table 8 represent the most favorable targets for future proton-radioactivity experiments.
Among these, ¹⁹⁵Ac, ²⁰⁰Pa, ²⁰⁶Np, ²¹²Am, and ²¹⁸Bk are predicted to exhibit the most accessible proton-decay
characteristics. Their relatively large proton-decay energies result in enhanced barrier penetrabilities and
calculated proton-decay half-lives in the range of approximately 10⁻⁷–10⁻⁵ S, which are compatible with the
capabilities of current high-efficiency decay-spectroscopy techniques. In addition, theoretical calculations
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indicate that proton emission is expected to compete successfully with α decay and spontaneous fission in these
nuclei, making them particularly attractive candidates for the first experimental observation of proton
radioactivity in the actinide region [35,36].
The heavier proton-rich isotopes ²²⁴Es, ²²⁹Md, and ²³⁵Lr also warrant detailed experimental investigation, despite
the increasing importance of spontaneous fission. These nuclei occupy the transitional region where proton
emission, α decay, and spontaneous fission coexist, providing an excellent opportunity to study how the
dominant decay mechanism evolves with increasing atomic number. Measurements of their decay properties
would improve our understanding of the interplay between Coulomb repulsion, shell effects, nuclear
deformation, and fission stability in the heaviest known nuclei.
The enhanced production capabilities and advanced detector technologies available at FRIB, FAIR, RIKEN, and
GANIL are expected to make these experimental investigations increasingly feasible. High-resolution silicon
detector arrays, efficient recoil separators, and modern digital data-acquisition systems will improve the
sensitivity for detecting weak proton-emission branches and enable precise measurements of decay energies,
half-lives, and branching ratios. Such experimental data are essential for validating theoretical models, including
the Coulomb and Proximity Potential Model (CPPM), and for refining predictions of proton radioactivity in
regions of the nuclear chart that remain experimentally unexplored [35,36].
Overall, the isotopes identified in Table 7 provide a well-defined roadmap for future investigations of proton
radioactivity in heavy nuclei. Their experimental confirmation would extend the known proton-emitting region
into the actinide domain, provide stringent tests of current theoretical models, and offer new insights into shell
structure, deformation effects, and the location of the proton drip line. These studies will represent an important
step toward understanding the stability of the heaviest proton-rich nuclei and will help guide future explorations
of the actinide and super heavy regions.
Table 6. Recommended Experimental Targets for Future Proton-Radioactivity Studies in Actinides
Nucleus
Q
p
(MeV)
Predicted
log
10
T
1/2
,p (S)
Predicted
T
1/2
,p (S)
Dominant Decay
Mode
Recommended
Facility
Reference
¹⁹⁵Ac
2.161
−6.7230
1.89 × 10⁻⁷
Proton decay
FRIB
[35,36]
²⁰⁰Pa
2.111
−5.9691
1.07 × 10⁻⁶
Proton decay
FAIR
[35,36]
²⁰⁶Np
1.911
−4.1216
7.56 × 10⁻⁵
Proton decay
RIKEN
[35,36]
²¹²Am
2.051
−4.6445
2.27 × 10⁻⁵
Proton decay
GANIL
[35,36]
²¹⁸Bk
2.241
−5.3828
4.14 × 10⁻⁶
Proton decay
FAIR
[35,36]
²²⁴Es
2.181
−4.5262
2.98 × 10⁻⁵
Spontaneous fission
FRIB / RIKEN
[35,36]
²²⁹Md
2.251
−4.5400
2.88 × 10⁻⁵
Spontaneous fission
FAIR
[35,36]
²³⁵Lr
2.161
−3.4850
3.27 × 10⁻⁴
Spontaneous fission
FAIR / GANIL
[35,36]
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CONCLUSIONS
Proton Radioactivity Has Emerged As One Of The Most Sensitive Probes Of Nuclear Structure Beyond The
Proton Drip Line, Offering Direct Insight Into Quantum Tunnelling In Proton-Rich Nuclei. Since Its
Experimental Discovery, Investigations Of Proton Emission Have Significantly Improved Our Understanding
Of Single-Particle Configurations, Shell Evolution, Nuclear Deformation, And The Interplay Between The
Attractive Nuclear Interaction And Coulomb Repulsion. Consequently, Proton Radioactivity Has Become An
Indispensable Spectroscopic Tool For Exploring Nuclei At The Limits Of Nuclear Stability.
Although experimentally established proton emitters are concentrated mainly in the rare-earth and heavy-mass
regions, theoretical investigations over the past two decades indicate that proton radioactivity may extend into
the actinide region. The large Coulomb fields, pronounced deformation, and coexistence of competing decay
channels make actinide nuclei an especially interesting testing ground for studies of exotic radioactive decay.
Systematic calculations suggest that several neutron-deficient isotopes between actinium (Z = 89) and
lawrencium (Z = 103) possess positive proton-decay energies and half-lives that could be accessible to future
experimental measurements.
This review has summarized the present understanding of proton radioactivity in actinide nuclei, including the
predicted proton emitters, their decay characteristics, competition with α decay and spontaneous fission, Geiger–
Nuttall-type systematics, and the performance of the principal theoretical models used to describe proton
emission. Comparative analyses indicate that models such as the Coulomb and Proximity Potential Model
(CPPM), the Effective Liquid Drop Model (ELDM), the Density-Dependent Michigan 3-Yukawa (DDM3Y)
interaction, the Generalized Liquid Drop Model (GLDM), and the Jeukenne–Lejeune–Mahaux (JLM) interaction
successfully reproduce the overall trends of proton-decay half-lives, with ELDM and DDM3Y generally
providing the highest predictive accuracy. The complementary use of these approaches has substantially
improved confidence in predictions for proton-rich nuclei that remain beyond current experimental reach.
Despite these theoretical advances, the experimental observation of proton radioactivity in actinide nuclei
remains an outstanding challenge. Extremely low production cross-sections, very short decay times, and the
increasing competition from α decay and spontaneous fission limit the accessibility of these exotic systems.
Nevertheless, continuous improvements in rare-isotope production, recoil-separation techniques, and high-
resolution decay spectroscopy are expected to overcome many of these difficulties. The capabilities of modern
facilities such as FRIB, FAIR, RIKEN, and GANIL provide realistic prospects for discovering the first proton-
emitting actinides and for testing long-standing theoretical predictions.
Future experimental studies will not only verify the existence of predicted proton emitters but will also provide
important information on shell structure, deformation effects, spectroscopic factors, and the evolution of nuclear
stability near the proton drip line. Measurements of proton-decay energies, half-lives, and branching ratios will
offer stringent tests of current theoretical models and contribute to a more comprehensive understanding of
charged-particle emission in heavy nuclei. In addition, extending these investigations toward the super heavy
region may reveal new manifestations of proton radioactivity and clarify the influence of shell stabilization in
nuclei approaching the predicted island of stability.
In conclusion, proton radioactivity in the actinide region represents an important frontier in contemporary
nuclear physics. The combination of increasingly sophisticated theoretical models and rapidly advancing
experimental capabilities is expected to drive significant progress in the coming years. Successful identification
of proton-emitting actinides would not only broaden the known limits of proton radioactivity but also provide
fundamental insight into the structure and stability of the heaviest proton-rich nuclei, thereby enriching our
understanding of the nuclear landscape at its extreme boundaries.
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