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We present some of the recent experimental results in heavy-ion transfer reactions obtained with the large solid angle magnetic spectrometer PRISMA at energies close to the Coulomb barrier. We focus on a series of experiments that have been carried out to study the nucleon-nucleon correlations for closed shell and superfluid systems. They are discussed together with the newest results concerning the proton transfer channels above and below the Coulomb barrier. The second set of the experiments was performed to study the production mechanism of heavy neutron-rich nuclei and the related effects of secondary processes.

We extend our Monte Carlo algorithm for generating global configurations in nuclei to include different spatial distributions of protons and neutrons in heavy nuclei, taking into account the difference of spatial correlations between two protons, two neutrons, and proton-neutron pairs. We generate configurations for Ca48 and Pb208 neutron-rich nuclei, which can be used in general-purpose high-energy A(e,e′p), p−A, and A−A event generators. As an application of lead configurations, we developed an algorithm for proton-heavy nucleus collisions at the CERN Large Hadron Collider for final states with a hard interaction in the channels where cross sections for p−p and p−n scattering differ. Soft interactions are taken into account in the color fluctuation extension of the Glauber algorithm, taking into account the inherently different transverse geometry of soft and hard p−N collisions. We use the new event generator to test an interesting observation of Paukkunen [Phys. Lett. B 745, 73 (2015)] that the ratio of W± production rates in p-Pb collisions should significantly deviate from the inclusive value for peripheral collisions due to the presence of a neutron skin. We qualitatively confirm expectation of Paukkunen, although, for a realistic centrality trigger, we find the effect to be a factor of 2 smaller than the original estimate.

The two-nucleon momentum distributions have been calculated for nuclei up to A=40 and various values of the relative and center-of-mass momenta and angle between them. For complex nuclei a parameter-free linked-cluster expansion, based upon a realistic local two-nucleon interaction of the Argonne family and variational wave function featuring central, tensor, spin and iso-spin correlations, has been used. The obtained results show that: 1) independently of the mass number A, at values of the relative momentum k_rel> 2 fm^{-1} the proton-neutron momentum distributions for back-to-back (BB) nucleons (K_cm=0) exhibit the factorization property n_A^{pn}(k_rel,K_cm=0)=C_A^{pn} n_D(k_rel) n_{cm}^{pn}(K_cm=0), where n_D is the deuteron momentum distribution, n_{cm}^{pn}(K_{cm}=0) the momentum distribution of the c.m. motion of the pair and C_A^{pn} the nuclear contact measuring the number of BB pn pairs with deuteron-like momenta; 2) the values of the proton-neutron nuclear contact C_A^{pn} are obtained in a model-independent way from the ratio n_A^{pn}(k_rel,K_cm=0)/n_D(k_rel) n_{cm}^{pn}(K_cm=0); 3) also the K_cm-integrated pn momentum distributions divided by the deuteron momentum distribution exhibits a constant behavior equal to C_A^{pn}, but only at very high values of k_{rel}> 3.5fm^{-1}, where the relative momentum distribution is entirely governed by BB short-range correlated nucleons; 4) the absolute value of the number of pn and pp short-range correlated pairs is calculated, illustrating that the high values (K_cm>1 fm^{-1}) of the pair c.m. momentum appreciably reduce the dominance of the pn over pp pairs produced by the tensor force when K_cm=0; 5) calculations are in good agreement with the VMC calculations for light nuclei and with available experimental on the processes A(e,e'pn)X and A(e,e'pp)X., 22 pages, 17 figures, 4 tables

The revival of transfer reaction studies benefited from the construction of the new generation large solid angle spectrometers, coupled to large γ arrays. The recent results of γ-particle coincident measurements demonstrate a strong interplay between single-particle and collective degrees of freedom that is pertinent to the reaction dynamics. By studies of transfer of pairs, valuable information on the component responsible for particle correlations has been derived.

Nucleon transfer reactions at energies close to the Coulomb barrier always played an important role in nuclear structure and reaction dynamics studies. It has been shown that heavy-ion reactions are an ideal tool for the study of the residual interaction in nuclei, in particular the components responsible for the couplings and correlations. The main subject of the present thesis is the study of the properties of the nuclear force which are not accounted for by the mean field description, especially the role played by neutron-proton correlations. This has been addressed by measurements of multinucleon transfer reactions performed with the new generation magnetic spectrometer PRISMA and its ancillary detectors. The experimental differential and total cross sections and total kinetic energy loss distributions for the final reaction products have been extracted and compared with the predictions of the GRAZING model for heavy-ion transfer reactions, based on semi-classical theory. The main objective was to search for an experimental signature of transfer of correlated neutron-proton pairs in the region near the Z =20 and N =20 shell closures. Through the simultaneous study of the absolute cross sections for all channels populated via transfer of nucleon pairs (±nn), (±pp) and (±np), and their comparison with the theoretical predictions, we explored the possible effect of (np) correlation. The findings have been also corroborated with results obtained at energies below the Coulomb barrier, where the excitation energies of the final reaction products are expected to be small. The comparison of the experimental results with the semi-classical calculations that include only the transfer of independent particles shows that the experimental cross section of (+1p+1n) channel is enhanced, indicating the possibility of a presence of a (np) pair degree of freedom. The analysis of these inclusive data was corroborated by a complementary analysis of γ-particle coincidences, where PRISMA has been used in coupled operation with the CLARA γ array. From the analysis of these coincidences, the population strength of excited states has been extracted for different transfer channels. In particular, for 42K, reached via the (+1p+1n) channel, a strong population of the 7+ state has been evidenced. Since this can happen when a neutron and a proton occupy the same f7/2 orbital, the finding may give a further support to the presence of a neutron-proton correlation. Reakcije prijenosa nukleona na energijama blizu kulonske barijere važne su i u proučvanju strukture jezgara i mehanizma reakcije. Pokazalo se da su teškoionske reakcije odličan način proučavanja rezidualne interakcije u jezgrama, naročito dijelova odgovornih za vezanje i korelacije. Glavna tema ovog doktorskog rada je proučavanje svojstava nuklearne sile koja nisu uključena u opis pomoću srednjeg polja, posebno uloga korelacija između neutrona i protona. To se proučavalo mjerenjem reakcije prijenosa mnogo nukleona s magnetskim spektrometrom velikoga prostornoga kuta PRISMA i njegovim pomoćnim detektorima. Dobiveni su diferencijalni i ukupni udarni presjek, raspodjela gubitka kinetičke energije za sve produkte reakcije, te su uspoređeni s teorijskim predviđanjima modela GRAZING. Glavna ideja je potraga za eksperimentalnim potpisom prijenosa koreliranog para neutron-proton u području blizu Z = 20 i N = 20 zatvorenih ljusaka. Istodobnom usporedbom apsolutnog udarnog presjeka za sve kanale koje su pobuđeni prijenosom para nukleona, (±nn), (±pp) i (±np), te njihovom usporedbom s teorijskim predviđanjima, traženi su mogući efekti (np) korelacija. Rezultati su potvrđeni s rezultatima dobivenim na energijama ispod kulonske barijere, gdje se očekuju male energije pobuđenja produkata reakcije. Usporedba mjerenih rezultata s polu-klasičnim računima koji uključuju samo prijenos neovisnih čestica pokazuje da je (+1p+1n) kanal pojačan, što može ukazivati na moguć doprinos (np) korelacija. Analiza inkluzivnih podataka je nadopunjena dodatnom analizom γ-fragment koincidencija, kada je PRISMA korištena s CLARA γ detektorom. Ove koincidencije omogućuju proučavanje snage pobuđenja različitih stanja. 42K kanal, pobuđen putem prijenosa jednog protona i neutrona, pokazuje jako pobuđenje 7+ stanja. Taj rezultat se može shvatiti kao dodatna potvrda prisutnosti korelacije neutron-proton, jer se 7+ stanje može opisati kao stanje u kojem su neutron i proton u istoj f7/2 orbitali.

We investigate the factorization properties of the exclusive electroinduced two-nucleon knockout reaction $A(e,e'pN)$. A factorized expression for the cross section is derived and the conditions for factorization are studied. The $A(e,e'pN)$ cross section is shown to be proportional to the conditional center-of-mass (c.m.) momentum distribution for close-proximity pairs in a state with zero relative orbital momentum and zero radial quantum number. The width of this conditional c.m. momentum distribution is larger than the one corresponding with the full c.m. momentum distribution. It is shown that the final-state interactions (FSIs) only moderately affect the shape of the factorization function for the $A(e,e'pN)$ cross sections. Another prediction of the proposed factorization is that the mass dependence of the $A(e,e'pp)$ $[A(e,e'pn)]$ cross sections is much softer than $\frac{Z(Z-1)}{2}$ $[NZ]$., Comment: 12 pages, 11 figures, 2 tables. Accepted for publication in PRC. Small differences in discussion throughout article ("scaling" replaced by "factorization")

An excitation function of one- and two-neutron transfer channels for the 60Ni+116Sn system has been measured with the magnetic spectrometer PRISMA in a wide energy range, from the Coulomb barrier to far below it. The experimental transfer probabilities are well reproduced, for the first time with heavy ions, in absolute values and in slope by microscopic calculations which incorporate nucleon-nucleon pairing correlations.

The reaction O-16(e, e'pp) has been studied at a transferred four-momentum (omega, \q\) = (210 MeV, 300 MeV/c). Evidence has been obtained for direct knockout of proton pairs from the 1p shell. The excitation-energy spectrum of the residual nucleus and the missing-momentum densities indicate that knockout of a S-1(0) pair dominates the reaction, while there is also a noticeable contribution from knockout of P-3 pairs.

Using realistic wave functions, the proton-neutron and proton-proton momentum distributions in $^3He$ and $^4He$ are calculated as a function of the relative, $k_{rel}$, and center of mass, $K_{CM}$, momenta, and the angle between them. For large values of ${k}_{rel}\gtrsim 2\,\,fm^{-1}$ and small values of ${K}_{CM} \lesssim 1.0\,\,fm^{-1}$, both distributions are angle independent and decrease with increasing $K_{CM}$, with the $pn$ distribution factorizing into the deuteron momentum distribution times a rapidly decreasing function of $K_{CM}$, in agreement with the two-nucleon (2N) short range correlation (SRC) picture. When $K_{CM}$ and $k_{rel}$ are both large, the distributions exhibit a strong angle dependence, which is evidence of three-nucleon (3N) SRC. The predicted center-of-mass and angular dependence of 2N and 3N SRC should be observable in two-nucleon knock-out processes $A(e,e'pN)X$., Comment: 5 pages, 5 figures

The transfer reaction for the {sup 116}Sn+{sup 60}Ni system has been studied using the PRISMA magnetic spectrometer at different bombarding energies from above to well below the Coulomb barrier. The experiment has been done in inverse kinematics and light target-like ions have been detected with PRISMA placed at very forward angles. Good mass, nuclear charge and kinetic energy resolutions have been achieved. Sufficient statistics has been accumulated to extract angular distributions for different bombarding energies have been extracted and the response function of the spectrometer has been studied to correct for the aberration due to the transport of the ions in PRISMA. The comparison between the present case and the previously measured {sup 96}Zr+{sup 40}Ca system, superfluid and near closed shells nuclei, respectively, should significantly improve our understanding of nucleon-nucleon correlation properties in multinucleon transfer processes.

Recent BNL and Jlab data provided new evidence on two nucleon correlations (2NC) in nuclei. The data confirm the validity of the convolution model, describing the spectral function (SF) of a correlated pair moving in the mean field with high and low relative and center-of-mass (cm) momenta, respectively. The model is built assuming that the wave function (WF) of a nucleus A, describing a configuration where the cm momentum of a correlated pair is low and its relative momentum is high, factorizes into the product of the two-body WF and that of the A-2 system. Such a factorization has been shown to occur in nuclear matter (NM). Here it is shown that few-body systems exhibit factorization, which seems to be therefore a general property, to be reproduced also in studies of the WF of finite nuclei., 4 pages, 4 figures, presented by S. Scopetta at the 21st European Conference on Few-Body Problems in Physics, Salamanca, Spain, 30 August - 3 September 2010, submitted to Few-Body Systems

A silicon detector system has been developed for proton detection in electron scattering reactions at MAMI. The use of digital alghoritms for detector signal processing enabled maintaining the acceptable energy resolution at high counting rates. Triple-coincidence reactions 12C(e, e'ppi-)11C and 12C(e, e'pp)10Be were studied, where in later, the differential cross section for the transition to berilium ground-state has been extracted. By comparison with theoretical models, this result could contribute to understanding of nucleon-nucleon correlations and thus the properties of atomic nuclei.

A silicon detector system has been developed for proton detection in electron scattering reactions at MAMI. The use of digital algorithms for detector signal processing enabled maintaining the acceptable energy resolution at high counting rates. Triple-coincidence reactions 12C(e, e´pπ-)11C and 12C(e, e´pp)10Be were studied, where in the latter, the differential cross section for the transition to berilium ground-state has been extracted. By comparison with theoretical models, this result could contribute to understanding of nucleon-nucleon correlations and thus the properties of atomic nuclei. Razvijen je sustav silicijskih detektora za opažanje protona u reakcijama elektronskog raspršenja na ubrzivaču MAMI. Za obradu detektorskih signala upotrijebljeni su digitalni algoritmi, čime je omogućeno zadržavanje prihvatljive energijske razlučivosti uz visoki tok čestica kroz detektorski sustav. Proučavane su trostruko-koincidentne reakcije 12C(e, e´ pπ-)11C, te 12C(e, e´ pp)10Be u kojoj je određen diferencijalni udarni presjek za prijelaz u osnovno stanje berilija. Taj bi rezultat, usporedbom s teorijskim modelima, mogao doprinjeti razumijevanju nukleon-nukleon korelacija, a time i svojstava atomske jezgre.

A silicon detector telescope has been developed for electron scattering experiments on nuclei at MAMI. It subtends relatively large solid angle (up to 88 msr) and is therefore suitable for measurements where larger acceptances are needed due to slower data collection. Digital processing of detector signals using variable-shaping-time algorithm enables maintaining good energy resolution even at high counting rates (< 500 kHz). A pilot measurement of the triple coincidence reaction 12C(e, e′ pp)10Be was made using the silicon detector along with two magnetic spectrometers and the preliminary results show satisfing missing mass resolution m = 0.56 MeV , with some 250 events in the ground state of 10Be.

This paper reports on measurements of the 3He(e, epp) reaction measured at AmPS and the 3He(e, epn) reaction measured at MAMI. The measurements were performed in similar kinematics to allow a comparison to be made between the cross sections of the two reactions. Results are shown for both reactions together with a comparison for the 3He(e, e epp) data with continuum Faddeev calculations.

Telescope of silicon detectors for proton detection in electron scattering experiments at MAMI is presented. Triple coincidence measurements and investigations of nucleon-nucleon correlations in nuclei is discussed.

After a brief overview of relevant studies on one-nucleon knockout showing the importance of quantitatively understanding the origin of the quenched spectroscopic factors extracted from data, attention is focussed on two-nucleon emission as a suitable tool to investigate nucleon-nucleon correlations inside complex nuclei. In particular, direct (e,e$'$pp) and (e,e$'$pn) reactions are discussed, and the role of final-state interactions is studied. The influence of the mutual interaction between the two outgoing nucleons is shown to depend on the kinematics and on the type of the considered reaction., Comment: 13 pages, 4 figures. Proceedings of 2nd Int. Conf. on Nuclear and Particle Physics with CEBAF at Jefferson Lab, Dubrovnik, 26-31 May 2003, to be published on Fyzika B

A semiclassical model is employed to study the effects of rescattering on (e,e˘p) cross sections. We consider a two-step process with the propagation of an intermediate nucleon and use Glauber theory to account for the effects of N-N scattering. This calculation has relevance for the analysis of data at high missing energies. Of particular interest is the E97-006 experiment done at JLab. It is found that rescattering is strongly reduced in parallel kinematics and that the excitation of nucleon resonances is likely to give important contributions to the final-state interactions in the correlated region., Primjenjujemo poluklasičan model za proučavanje učinaka dodatnih raspršenja u udarnim presjecima reakcija (e,e′p). Razmatramo dvostruki proces s gibanjem međunukleona, a učinke N–N raspršenja uključujemo prema Glauberovoj teoriji. Ovi su računi važni za analize podataka pri velikim manjkovima energije. Posebno je zanimljivo mjerenje E97-006 u JLaboratoriju. Nalazimo jako smanjenje dodatnih raspršenja u usporednoj kinematici te vjerojatno velike doprinose od uzbude nukleonskih rezonancija međudjelovanju u konačnom stanju u koreliranom području.

Nucleon-nucleon correlations, especially those of short-range character, can be well studied with electron-induced two-nucleon knockout reactions at intermediate electron energies. However, these reactions are not only driven by one-body currents, i.e., coupling of the virtual photon to one of the nucleons of a correlated pair, a process that directly probes NN-correlations. Also two-body currents, resulting from intermediate Delta-excitation and coupling to exchanged mesons, as well as final state interactions, influence the experimental cross section. Exclusive measurements of the three-body breakup of 3He offer the opportunity to compare data to microscopic calculations. The relative importance of competing two-proton knockout mechanisms can be investigated by varying the energy and momentum of the virtual photon. The experiment was performed with the electron beam extracted from the Amsterdam Pulse Stretcher (AmPS) at NIKHEF; the incident electron energy was 564 MeV. A cryogenic, high-pressure 3He gas target was used with a thickness of 270 mg/cm^2. Scattered electrons were detected in the QDQ magnetic spectrometer and both emitted protons in the HADRON plastic scintillator arrays. Cross sections were determined for three values of the three-momentum transfer of the virtual photon (q=305, 375, and 445 MeV/c) at an energy transfer value omega of 220 MeV. At q=375 MeV/c, measurements were performed over a continuous range in energy transfer from 170 to 290 MeV. The data are compared to results of continuum-Faddeev calculations performed by Golak et al., that account for rescattering among the emitted nucleons. Various potential models were used in the calculations: Bonn-B, CD-Bonn, Nijmegen-93 and Argonne v18 . Presentation of the data as a function of the missing or neutron momentum, pm, shows that the cross section decreases exponentially as a function of pm. Calculations performed with only a one-body hadronic current operator show fair agreement with data obtained at pm < 100 MeV/c at omega = 220 MeV for all q-values. It can therefore be concluded that at omega = 220 MeV and pm < 100 MeV/c the cross section is dominated by direct knockout of two protons via a one-body hadronic current. At higher neutron momentum values, data and theoretical predictions differ up to a factor of five for all values of omega. Within the range of energy transfer values probed in this experiment, the high pm domain is expected to be strongly influenced by intermediate excitation in the proton-neutron pair. Within specific regions of phase space, where two nucleons are emitted with comparable momentum vectors, rescattering processes strongly influence the cross section. For a such a region, measured at q=445 MeV/c, good agreement was found between data and the continuum- Faddeev calculations as a function of the pn momentum difference in the final state. Information on the wave function of 3He may be obtained in the domain omega = 220 MeV and pm < 100 MeV/c by representing the cross section as a function of pdiff1, which can be related to the relative momentum of the constituents of the two-proton pair in the initial state. The observed decrease of the cross section reflects the behaviour of the wave function and is well reproduced by calculations. At present, the data do not permit to express preference for any one of the potential models considered.

Nucleon-nucleon correlations, especially those of short-range character, can be well studied with electron-induced two-nucleon knockout reactions at intermediate electron energies. However, these reactions are not only driven by one-body currents, i.e., coupling of the virtual photon to one of the nucleons of a correlated pair, a process that directly probes NN-correlations. Also two-body currents, resulting from intermediate Delta-excitation and coupling to exchanged mesons, as well as final state interactions, influence the experimental cross section. Exclusive measurements of the three-body breakup of 3He offer the opportunity to compare data to microscopic calculations. The relative importance of competing two-proton knockout mechanisms can be investigated by varying the energy and momentum of the virtual photon. The experiment was performed with the electron beam extracted from the Amsterdam Pulse Stretcher (AmPS) at NIKHEF; the incident electron energy was 564 MeV. A cryogenic, high-pressure 3He gas target was used with a thickness of 270 mg/cm^2. Scattered electrons were detected in the QDQ magnetic spectrometer and both emitted protons in the HADRON plastic scintillator arrays. Cross sections were determined for three values of the three-momentum transfer of the virtual photon (q=305, 375, and 445 MeV/c) at an energy transfer value omega of 220 MeV. At q=375 MeV/c, measurements were performed over a continuous range in energy transfer from 170 to 290 MeV. The data are compared to results of continuum-Faddeev calculations performed by Golak et al., that account for rescattering among the emitted nucleons. Various potential models were used in the calculations: Bonn-B, CD-Bonn, Nijmegen-93 and Argonne v18 . Presentation of the data as a function of the missing or neutron momentum, pm, shows that the cross section decreases exponentially as a function of pm. Calculations performed with only a one-body hadronic current operator show fair agreement with data obtained at pm < 100 MeV/c at omega = 220 MeV for all q-values. It can therefore be concluded that at omega = 220 MeV and pm < 100 MeV/c the cross section is dominated by direct knockout of two protons via a one-body hadronic current. At higher neutron momentum values, data and theoretical predictions differ up to a factor of five for all values of omega. Within the range of energy transfer values probed in this experiment, the high pm domain is expected to be strongly influenced by intermediate excitation in the proton-neutron pair. Within specific regions of phase space, where two nucleons are emitted with comparable momentum vectors, rescattering processes strongly influence the cross section. For a such a region, measured at q=445 MeV/c, good agreement was found between data and the continuum- Faddeev calculations as a function of the pn momentum difference in the final state. Information on the wave function of 3He may be obtained in the domain omega = 220 MeV and pm < 100 MeV/c by representing the cross section as a function of pdiff1, which can be related to the relative momentum of the constituents of the two-proton pair in the initial state. The observed decrease of the cross section reflects the behaviour of the wave function and is well reproduced by calculations. At present, the data do not permit to express preference for any one of the potential models considered.