Nuclear resonance fluorescence (NRF) denotes the process of resonant excitation of definite nuclear states of a target nucleus by absorption of electromagnetic radiation (real photons) and subsequent decay of these levels by re-emission of the equivalent radiation. A simplified scheme of an NRF experiment with photons from bremsstrahlung production is shown in fig. 1.

Fig. 1. Sketch of Nuclear Resonance Fluorescence experiments with bremsstrahlung.

The electron beam of the accelerator hits the radiator and generates a continuous (in energy) bremsstrahlung spectrum with a maximum photon energy according to the electron energy. The bremsstrahlung photons are used to excite resonantly the NRF target nucleus under investigation. Such NRF experiments using bremsstrahlung of relativistic electrons represent an outstanding tool for a precise and systematic investigation of the structure of stable nuclei and for a model-independent determination of lifetimes in the femtosecond (fs) region. In particular, low-multipolarity (electric and magnetic dipole) transitions can be efficiently studied favoured by the low detection limit of the NRF method.

The energies E_x of the excited states, their lifetimes t (or - what is equivalent - their energy widths DE_x or G), their angular momenta J and their parities p provide important information about the nuclear structure, and - thus - about the fundamental forces between the nuclear constituents.

The advantage of this method : Both the excitation and the de-excitation processes proceed via the electromagnetic interaction - the best understood interaction in physics.

In order to efficiently perform such experiments, a high beam intensity of unpolarized as well as linearly polarized bremsstrahlung and excellent background conditions are needed in combination with highly efficient, high-resolution Ge detectors. A typical thin(!)-target bremsstrahlung spectrum generated by the GEANT-3.21 code is shown in fig. 2 . This spectrum simulates the experimental conditions very well.

Fig. 2. GEANT simulation of a thin-target forward-angle bremsstrahlung spectrum (radiator: 25 mm Al, E_e=10 MeV).

The process of resonant absorption and subsequent re-emission of real photons and the quantities that influence the corresponding photon scattering cross sections are illustrated in fig. 3 [1,2]. Here, J_i, J and J_f are the spins of the initial, intermediate and final states, respectively. The initial state in NRF experiments corresponds to the ground state [J_i = Jo]. The multipolarities L_n(with n = 1,2) refer to the transitions involved. The cross section s for the absorption and subsequent re-emission of a photon from the ground state with spin and parity J_o^p to some excited state J^p and back to the ground state or a low-lying state J_f^p has a resonance shape and is of Doppler-broadened Breit-Wigner type {cf. [3] }.

Fig.3. Definitions of multipole orders, decay widths and spins.

In our NRF experiments, a continuous bremsstrahlung source is used. Therefore, the energy-integrated differential cross section I_s is determined in the experiments. It can be expressed in terms of the ground state (G_o) and final state (G_f) transition strengths as well as the total transition strength (G). I_s depends also on the energy of the bremsstrahlung photons and on the angular correlation of the scattered photons with respect to the incoming photons. G is connected with the lifetime t of the excited state via

Hence, half-lives of a few fs can easily be measured with the NRF method.

The de-excitation of the excited states can be observed with semiconductor (e.g. CLUSTER or HP Ge) detectors placed at different angles (e.g. 90^o and 127^o in the case of even-even nuclei) to determine the multipolarities of the transitions and, thus, the spins of the corresponding levels. This procedure is based on the different angular distributions of the scattered photons, which vary with their multipolarity {cf. [1] }.

A typical NRF spectrum measured for the de-excitation of ⁸⁸Sr in the (g, g') reaction with two EUROBALL cluster detectors at an endpoint energy of 6.8 MeV bremsstrahlung at the S-DALINAC accelerator [4] is displayed in fig. 4.

Fig. 4. A portion of the total g-ray spectrum measured in the ⁸⁸Sr (g, g') ⁸⁸Sr reaction (cf. text and [4] for details).

For parity assignments to the excited levels, which are of decisive importance for the physical interpretation, the linear polarization of the photons is utilized. There are two methods for measuring this quantity:

The first technique (i) uses the partially linearly polarized off-axis bremsstrahlung {cf. [5,6] }. This is illustrated in fig. 5. The off-axis bremsstrahlung is selected by a fixed collimator on the beam axis by changing the angle of incidence q_o of the electrons onto the radiator by steering coils. This method is restricted to higher-energy photons (> 5 MeV) because of the low degree of polarization (10-30 %).

The second technique (ii) based on Compton polarimeters is an appropriate alternative and it employs the sensitivity of the Compton scattering process to the linear polarization of the scattered photons {cf. [7] }, especially in the lower-energy range (< 5 MeV).

Set-Up for NRF Experiments at ELBE

The set-up designed for NRF experiments with unpolarized and linearly polarized bremsstrahlung at ELBE is schematically displayed in fig. 6. The electron beam is transported by a non-dispersive dipole/quadrupole magnetic system and focused onto a thin (25-100 mm Al) bremsstrahlung radiator. The steering coils in front of the radiator enable the incidence polar and azimuthal angles of the electron beam to be changed in order to optimize the generation of linearly polarized photons. After passing through the thin radiator, the electrons are finally deflected by a 45^o dipole magnet into a beam dump. The (unpolarized as well as linearly polarized off-axis) bremsstrahlung photons produced in the radiator will be collimated and directed onto the scattering (NRF) target located about 4m downstream in the experimental hall. This geometry should ensure favourable background conditions. The g-rays scattered off the NRF target are detected with a EUROBALL Cluster module {see e.g. [8]} or by large-volume Ge detectors with about 100 % relative efficiency representing very powerful instruments for NRF experiments in the energy region of interest (about 1 to 15 MeV).

Fig. 6. Polarized-bremsstrahlung facility at ELBE.

A 1.6 m thick wall of baryt concrete blocks separates the experimental area from the electron beam line with radiator chamber and beam dump. This thorough shielding and the 2.6 m long collimator (fig. 7) will efficiently reduce the undesired photon and neutron background. The collimator features a step-like construction with a conic, slightly increasing aperture and is made from pure aluminium because of its high neutron separation energy of 13 MeV Those bremsstrahlung photons that have passed the NRF target are finally absorbed in a special g-dump (water tank partially shielded with Pb/Cd) and thus mostly removed from the experimental area. The actual beam energy (up to about 15 MeV) will be carefully adapted to the neutron separation energies of the radiator and collimator materials in order to avoid resp. minimize neutron production. The same applies to the ultra-high vacuum end flange (behind the 45^o dipole magnet) that is inevitably crossed by the primary bremsstrahlung photons. It will also be attempted to suppress the neutron background by utilizing time-of-flight techniques favoured by the large distance between radiator and NRF target and by the time structure of the electron beam. With average beam currents in the order of 500 mA (in the cw regime), photon fluxes of 5 x 10⁷ photons per MeV·s for 7 MeV photons at E_e^- = 10 MeV are expected at the NRF interaction area. The energy deposition in the thin radiator foil does, thereby, not exceed about 30 W and will be removed by water cooling.

Fig. 7. Sketch of the collimator for the photon beam.

Dipole Excitations in Medium-Mass Nuclei

The direct determination of the energy widths G of the excited nuclear states via the g-ray intensities of the de-exciting transitions is advantageous compared to other spectroscopic methods. According to eq. (1), the lifetimes of the corresponding levels can be deduced from these measurements.

In the energy range of ELBE, the incident photons predominantly transfer one unit of angular momentum to the target nucleus: DJ = 1. Therefore, the NRF experiments will be particularly selective for dipole excitations and represent an appropriate tool to investigate low spin states. With smaller probability, quadrupole excitations (DJ = 2) may be observed as well. In even-even nuclei (with ground state spin J = 0), only dipole states (J = 1) of both signs of parity can be excited. In this way, electric (1^-) and magnetic (1⁺) dipole excitations can be selectively investigated. We emphasize that the different parities characterize two completely different modes of excitation.

In the domain of the electromagnetic dipole excitations, spectroscopic experiments have revealed new, unexpected phenomena in recent years: Large magnetic dipole (M1) strengths have been discovered in heavy deformed nuclei [9]. The corresponding excitations have been associated with scissors-like oscillations of the deformed proton density distribution against the neutron distribution, and the excitation mode was, accordingly, called "scissors mode" (fig. 8).

Fig. 8. Scissors mode.

Large electric dipole (E1) transitions to the ground states have been observed in spherical nuclei near Z = 50 and N = 82. They are assumed to arise from the coupling of quadrupole and octupole vibrational modes of the nucleus.

In medium-mass nuclei (A60 - 130), however, dipole excitations have been scarcely investigated. In this region, the existence of the scissors mode has been proven only in ⁹⁴Mo [10] and ⁸⁸Sr [11]. Here, this mode generally competes with other transitions (e.g. of spin-flip type) between shell model states. The determination of the relative weights of these two excitation mechanisms turns out to be a theoretical and experimental challenge.

Variations of the nuclear shape between spherical and deformed mass distributions are expected even with minor changes in the nucleon numbers - a typical feature of medium-mass nuclei, which are candidates for future investigations in NRF experiments at ELBE. The evolution of the scissors mode with the transition from spherical to deformed nuclei will be studied.

The experimentally observed fragmentation of magnetic and electric dipole strengths needs to be investigated systematically, especially in odd-mass nuclei. The theoretical understanding of this phenomenon remains a challenge. In particular, only the spectral region of 3 - 8 MeV has been studied experimentally mainly in other mass regions than the one in consideration (A60 - 130). Furthermore, little is known in the energy range above 8 MeV up to about 15 MeV. There are several questions that need to be answered, for example: Do multi-phonon excitations contribute to the dipole strenghts (cf. fig. 9)?

Fig. 9. Dipole excitations in medium-mass nuclei.

Also, the question of the existence of a low-lying E1-Pygmy resonance is not yet investigated in detail.

An essential point will, thereby, be the parity measurements of the excited states up to higher energies. The ELBE set-up should be particularly suited for solving this task.

The permanent support by the Rossendorf theory group is essential. An appropriate RPA model has been developed and refined in Rossendorf during the past years, where, in particular, multi-step processes of de-excitation have been included carefully.

The scientific program for NRF experiments at ELBE will contribute to most of these important aspects of nuclear structure research. The first experimental proposals regarding the N = 50 nuclei ⁸⁸Sr, ⁸⁹Y and ⁸⁷Rb have already been formulated.

References

[1]   U. Kneissl et al., Progr. Part. Nucl. Phys. 37 (1996) 349
[2]   C. Fransen, Diploma Thesis (1997) Univ. zu Koeln
[3]   F.R. Metzger, Progr. Nucl. Phys. 7 (1959) 54
[4]   L. Kaeubler et al., Ann. Rep. 1997, Rossendorf, FZR-215 (1998) 53
[5]   U.E.P. Berg and U. Kneissl, Rev. Nucl. Part. Sci. 37 (1987) 33
[6]   K. Govaert et al., Nucl. Instr. and Meth. A 337 (1994) 265
[7]   B. Schlitt et al., Nucl. Instr. and Meth. A 337 (1994) 416
[8]   R. Schwengner et al., Nucl. Phys. A 620 (1997) 277
[9]   A. Richter, Proc. Int. Conf. on Nucl. Phys. Florence (1983) vol.2, p. 189;
       D. Bohle et al., Phys. Lett. 137 B (1984) 27
[10] N. Pietralla et al., Phys. Rev. Lett. 83 (1999) 1303
[11] L. Kaeubler et al., Eur. Phys. J. A7 (2000) 15; L. Kaeubler et al., to be published