Low energy nuclear transitions initiated by
femtosecond laser plasma
A.B. Savel'ev, A.V.Andreev, V.M.Gordienko, and P.M.Mikheev
International Laser Centre & Physics Faculty, M.VLomonosov Moscow State University, Vorobyevy gory,
Moscow, 119899,Russia,Phone:7(095)9395318;Fax:7(095)9393113;e-mail:savelev@femto.phys.msu.su
Abstract: We discuss origins of low energy nuclear transitions taking place at irradiation of solids
with moderate intensity femtosecond laser pulses. Possible applications of these phenomena to
population inversion on nuclear transitions are also presented.
INTRODUCTION
During past few years nuclear physics with ultra short laser pulses became one of the
most "hot" and intensively investigated area of super strong laser-matter interaction1. A
wide range of nuclear processes was observed experimentally: from nuclear fusion and
fission to photo-excitation and positron production. Among them, there exist nuclear
processes initiated by electrons, x-rays or ions of less than few tenths of keV energy. Such
processes we would further refer as low energy nuclear processes. One does not need
relativistic intensities to enter this regime of femtosecond laser-matter interaction with
solids: even at intensities of 1016-1017 W/cm2 hot electron temperature ranges from 3 up to
10 keV. Accelerated fast ions gain nearly the same energy per nucleon from these
electrons. Moreover it is someway "optimal" to use moderate intensities for low energy
nuclear processes initiation in plasma, and relativistic intensity regime seems even
useless. Thus, under irradiation of solids by femtosecond laser pulses at intensity around
1016 W/cm2 X-ray photo-excitation of 6.238 keV level of 181Ta nuclei took place2. At the
same conditions neutrons emerging from DD fusion in structured D-enriched Ti target3
were detected.
In this paper, we discuss experimental and theoretical aspects while initiating low
energy nuclear transitions in solids using moderate intensity laser pulses. We start by
presenting our data for thorough characterization of hot electrons production under
moderate intensity femtosecond laser-plasma interaction. We then move to discussion of
low energy nuclear transition excitation by plasma x-rays. Finally we discuss two-, threeand four level schemes for population inversion on nuclear transitions of 1-30 keV
energy.
CP634, Science of Superstrong Field Inter actions, edited by K. Nakajima and M. Deguchi
© 2002 American Institute of Physics 0-7354-0089-X/02/$ 19.00
115
EXPERIMENTAL CHARACTERIZATION OF HOT ELECTRONIC
COMPONENT
In our experiments we characterize hot electrons production under femtosecond laserplasma interaction by three different methods: by direct detection of hot electrons
escaping from plasma, with the help of double-channel x-ray scheme 4, and from time-offlight ionic measurements.
Figure 1 sketches our experimental setup. P-polarized radiation (200 fs, 616 nm) was
tightly focused onto flat target at 45° angle of incidence with maximum intensity up to
3-1016 W/cm2. Energy contrast ratio of the pulses was better than 1000 that yield in better
than 5 orders for intensity contrast. Target was placed inside vacuum chamber with
residual pressure less than 10" Torr. Different diagnostics were placed around the target.
Fig.l Experimental set up for hot electron component study.
x-ray detector
Focusing
lense F/D-6
Ionic TOP
Electronic
spectrometer
X-ray detector
Two hard x-ray detectors equipped with different filter sets were mounted out of the
vacuum chamber looking at the target through beryllium windows 100 jim thick. Double
channel x-ray detection scheme and algorithms providing for hot electron temperature
assessment in a single laser shot were described elsewhere 4'5. Simple ionic time-of-flight
(TOP) spectrometer consists of chevron-type double plate MCP detector VEU-7 was
placed 22 cm apart from the target along the target normal. This enables measurement of
ion velocities up to 5x108 cm/s .
Direct detection of electronic plasma currents was realized with special spectrometer
providing for both time-of-flight and energy resolution capabilities. It consists of
cylindrical capacitor-like half-circle energy analyzer with energy resolution of 8% and
detection range of 0.1-40 keV. This analyzer having itself 25 cm electron path was placed
50 cm apart from the target. Its entrance diaphragm was right up on the target normal.
Electron detection was fulfilled with chevron-type double-plate MCP detector VEU-7.
116
Fig.2 presents results from double-channel x-ray detection scheme in the case of Si
target. Characteristic slope of the curve E2~f'8 corresponds well to the known data and
theoretical predictions if laser energy absorbed in anomalous skin-effect regime 7. Here
we are using quantity "mean energy" instead of "electron temperature" because the latter
could be defined provided hot electrons follow maxwellian type distribution, that is
natural only for a system in equilibrium. At the same time, quantity "mean energy" is
applicable for any electron ensemble regardless of exact form of the distribution function.
Moreover, within frames of our algorithms special filter choice makes assessment of £2
nearly independent on exact distribution form 5 .
Fig. 2 Dependence of mean energy of hot electrons E2 on laser intensity / estimated by double channel hard
X-rays yield (o) and ionic TOP measurements (•).
<E2>, keV
8642-
0
I, PW/crrf
10
15
20
Ionic TOP measurements allow within frames of simple model of plasma expansion
estimating both energy £2 and also the ratio of thermal to hot electron concentration 5.
Figure 2 displays E2 estimation from ionic TOP measurements. The coincidence of the
this estimate with the one obtained by double-channel x-ray detection is excellent.
Finally we made direct detection of hot electron spectrum by electron analyzer. Figure
3 shows such a spectrum at laser pulse intensity of 2x1016 W/cm2. Fit of experimental
data was done by the bi-Maxwellian function. This gives values of thermal electrons
mean energy <L5r;>~300±100 eV, hot electrons mean energy <E2>~9±4 keV. These
values reasonably fits to the data plotted in the Figure 2.
LOW ENERGY NUCLEAR EXCITATION
Among other low energy nuclear processes, the isomeric level excitation seems the
most interesting one because of both fundamental physics involved and a wide set of
possible applications. First, even for low energy levels of stable isotopes their
characteristics could be still shady or yet unknown (for example only calculations exists
117
for both lifetime and conversion coefficient of 201Hg 1.56 keV nuclear level). Usually,
still fewer data are known for metastable isotopes. These mean that excitation in hot dense
laser plasma could provide for new methods of nuclear spectroscopy of low energy
nuclear levels.
Fig. 3. Electronic spectrum of laser plasma at I~2xl016 W/cm2, X=616 nm. Solid line - bi-maxwellian fit:
7>350 eV, T2=6 keV.
N9, a.
100
10
12
0
15
E, keV
Electrons and X-rays emitted under a femtosecond laser -plasma interaction can not
only initiate nuclear reactions but also excite nuclear levels. These processes are of
interest for a number of promising applications such as the isotope separation8 and the
creation of population inversion9. In particular, X-rays emitted by the USP plasma can be
efficiently used for excitation of metastable isotopes to the closely spaced level
accompanied by its decay to the ground state. This was realized in paper10 , where the
metastable level of 178Hf with the energy of 2.446 MeV and the lifetime of 31 year was
excited with a cw X-ray tube.
To our knowledge, no experiments have been performed in this field so far at
relativistic intensities. The hot-electron temperature reaches 10 keV already at a moderate
intensities, which is sufficient for direct excitation of low-lying nuclear levels of both
stable and metastable isotopes (we call the nuclear levels with energy Eg < 20 keV the
low-lying nuclear levels). The standard methods of nuclear spectroscopy of such levels
are based on the indirect population via the states with energy £y> 100 keV using electron
and ion accelerators n or on the direct photoexcitation using synchrotron radiation
sources12'13. Note that the parameters of low-lying nuclear levels are often unknown (even
when the ground state of a nucleus is stable) (see Table 1).
For metastable isotopes, the situation when a number of parameters are unknown is
encountered even more often. An important positive factor is that the low-lying nuclear
levels in a plasma are excited "instantly' because the relation Tg>TP is satisfied (xg is the
total lifetime of the excited state and Tp is the lifetime of a hot dense plasma). The
possibility of excitation of low-lying nuclear levels in the laser plasma has been discussed
over twenty years14'15'16. Experimental attempts to use the low- density laser plasma were
118
scarce17' 18 and unsuccessful19. The main problems are related to the low efficiency of
excitation by nanosecond laser pulses because of a low electron temperature of the plasma
and its low density. The plasma arisen from femtosecond laser plasma interaction is free
from these disadvantages and it has at the same time a sufficiently high electron
temperature and the nuclear density that is close to that of a solid.
Table 1. Low lying nuclear level data for stable isotopes: £y -excitation energy, M -moment and
parity, Ty - full half-lifetime, ft - internal conversion coefficient, O - transition multiplicity.
Isotope
£ r keV
M
T r ,ns
n
P
1.556
1/2-
1-10
M1+E2
(2-5)-104
6.238
9/2-
6050
El
70.5
8.4103
3/2+
4.08
M1+E2
285
9.396
7/2+
147
M1+E2
17.09
l
9.746
3/2-
2.38
M1(+E2)
264
HGC
13.275
5/2+
2950
E2
1120
57Fe
14.4129
3/2-
98.3
M1+E2
8.56
21.541
7/2+
9.6
M1+E2
28
wl
Hg
181j
169™m
69*
S3
Kr
%0s
l
l\Eu
The low-lying nuclear levels in the laser plasma can be excited via different channels,
both nuclear-electronic and nuclear-photonic, but the excitation by X-rays emitted by the
plasma dominates in the hot dense femtosecond plasma.
POPULATION INVERSION SCHEMES FOR NUCLEAR TRANSITIONS
The study of low-lying nuclear levels of metastable isotopes substantially expands the
field of investigations. One of the problems can be a search for candidates suitable for the
production of population inversion at nuclear transitions. One can see from Table 1 that
the lifetime of low-lying nuclear levels greatly exceeds that of the plasma, so that the
population inversion can be produced during the plasma lifetime. At the same time, to
obtain the population inversion for the nuclear level with energy less than 10 keV, when
the nuclear density is close to the density of a solid, the X-ray intensity within the nuclear
transition band should be >1016 W cm"2, which corresponds to the laser radiation intensity
I > 1021 W cm"2. For such intensities, the electron temperature exceeds 10 MeV and it
strongly differs from the optimal temperature Th ~ £y for the energy range of transitions
under study. From the point of view of observation of stimulated emission at nuclear
transitions, the isotopes presented in Table 1 can be divided into two groups. In the case
of nuclei with the high conversion coefficient at the transition to the ground state (201Hg,
119
181
Ta, 169Tm, 187Os, 73Ge), one can hope to obtain generation only in a plasma layer
containing ions with a high degree of ionization, because the 1C process can be
completely or strongly suppressed in this case. In the case of isotopes with a relatively
low conversion coefficient (83Kr, 57Fe, 161Dy), it is preferable to attempt to produce
inversion in a solid sample. Such an inversion can be achieved, for example, using a
multicomponent target consisting of a metal foil emitting X-rays and an active body,
which has no thermal contact with the foil. This substantially decreases the Doppler
broadening and allows, in principle, the development of schemes of the Mossbauer
gamma laser.
When ultrashort relativistic laser pulses are used, the hot-electron temperature achieves
several hundreds of keV, providing the possibility for excitation of higher-lying nuclear
levels. Consider nuclei of isotopes 73Ge, 83Kr (Table 2), and 107Ag, Ag, 119Sn. These
nuclei have a number of common features. First, the radiative decay of the first two
excited levels is cascade, i.e., the gamma transition from the second excited level occurs
to the first level, whereas the transition to the ground state is forbidden. Second, all the
isotopes have a long-lived isomeric state with the lifetime of the order of 1 s and longer.
Third, these transitions have a rather high electron con- version coefficient. In the scheme
for producing the population inversion under study, the temperature Th should provide
cascade excitation of the second nuclear level by X-rays emitted from the plasma or its
direct excitation due to inelastic electron scattering. The expanding plasma containing
highly ionized ions is deposited on a surface where the ions are completely neutralized.
During the lifetime of isotopes 73Ge, 83Kr, and 119Sn in the second excited state, a rather
large number of nuclei can be produced in the isomeric state. The ions formed due to the
conversion decay at the 2^1 transition are pulled out by a focusing electric field and are
deposited on a substrate, where the active body of a gamma laser is formed.
The population inversion can also be achieved for the four-level lasing schemes (153Eu,
Table 2). In this case, nuclei at the level 2 are selected due to the conversion decay at the
3 ^ 2 transition, while the lasing should occur at the 2 —> 1 or 2 —> 0 transition. A
substantial difference of the four-level scheme from the three- level scheme is, for
example, the fact that the third excited level of isotopes 13Eu,l Gd, and 189Os is coupled
with the ground state of the nucleus by a radiative transition having a low conversion
coefficient. Therefore, the nucleus can be excited to the third level in a multi-component
target by filtered X-rays emitted by the laser plasma, which excludes the necessity to
neutralize plasma ions. Another advantage of the four-level scheme with the 2 —> 1 lasing
transition is that this scheme is insensitive to the presence of nuclei in the ground state in
the active region of the gamma laser. This substantially decreases technological
requirements imposed on the process of preparation of the active region.
Among stable isotopes with low-lying nuclear levels with energies less than several
hundreds kiloelectronvolts there are isotopes that permit the use of three- and four-level
lasing schemes, which are typical for the visible range. The first five excited levels in the
161
Dy isotope are coupled by radiative transitions with the ground state and, therefore,
they can be excited by laser plasma X-rays (see Figure 4). It seems that the most
120
Table 2. Low lying nuclear levels of isotopes: e'y and Iy y transition energy and intensity.
Isotope
HGe
83 ^
36Kr
l53
Eu
M
n
Y transition
0
9/2+
13.275
66.716
68.752
68.752
0
5/2+
1/2(7/2)+
(7/2)+
9/2+
2950
0.499 s
1.74
1.74
E2
M2
100
100
M1+E2
9.396
41.543
0
7/2+
1/25/2+
147
1.83h
83.36720
97.43103
97.43103
103.1801
6
103.1801
6
7/2+
5/25/23/2+
3/2+
ft
100
13.275
53.440
55.42
68.752
0.227
M1+E2
E3
100
100
9.396
32.1473
17.09
2035
0.793
0.198
0.198
3.85
M1+E2
El
El
E2
100
0.12
100
83.36717
14.06383
97.43100
19.81296
3.82
11.2
0.307
3290
3.85
M1+E2
100
103.18012
1.72
1120
8.67
promising are the transitions terminating on the second excited level because the lifetime
of this level (0.83 ns) is 35 times shorter than that of the first excited state. The 171Yb
isotope is of great interest for the development of lasing schemes for nuclear transitions
because its third excited level with energy of 95.272 keV has a lifetime of 5.25 ms. This
level is coupled by the radiative transition only with the second excited level with energy
of 75.878 keV. However, the third level can be excited due to inelastic electron -ion and
ion - ion collisions or due to the radiative transition via the fourth excited level with
energy of 122.418 keV. The latter level is coupled with the third level by an intense
radiative transition with the multiplicity El.
CONCLUSIONS
Thus hot electrons produced under interaction of femtosecond laser pulses with dense
plasma gain enough energy to excite nuclear transitions in wide range of stable and
metastable isotopes and isomers. At laser intensities above 10 PW/cm2 mean energy of
hot electrons reaches 6-8 keV providing for generation of hard x-rays up to 10-20 keV.
X-ray photoexcitation of low energy nuclear levels could be treated as new tool for
nuclear spectroscopy of such levels. Besides, different schemes for population inversion
on gamma-transitions can be proposed, while more consecutive treatment of these ideas
suffers from luck of nuclear data on low lying nuclear levels.
121
ACKNOWLEDGEMENTS
This work was supported by Russian Foundation for Basic Research (grants ## 00-0217302,02-02-17138a, and 02-02-06104) and in part by BOARD.
Fig.4. Photoexcitation and decay of 1 *Dy isotope.
5 _________ 103.06 keV
100.46keV
: 74.57 keV; 3/2"; 3.14ns
2 — — ^J I—— 43.82 keV; 7/2+; 0.83 ns
. ———————— 25.65 keV; 5/2"; 29 ns
; OkeV;5/2+; stable
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