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Relational language is thought to influence mathematical skills. This study examines the association between relational language and number relation skills-knowledge of cardinal, ordinal, and spatial principles-among 104 U.S. kindergartners (5.9 years; 44% boys; 37% White, 25% Black, 14% Asian, 24% other) in the 2017-2018 academic year. Controlling for general verbal knowledge, executive function, and counting and number identification skills, relational language predicted later number relation skills, specifically number line estimation, β = .30. Relational language did not differentially predict number line estimation performance in children with low or high number relation skills, likely due to the restricted ranges of data within subgroups. Number relation skills, specifically number line estimation and number ordering, may be a pathway between relational language and mathematical skills.

12C +12 C is the main reaction during core and shell carbon burning in massive stars, however, at temperatures higher than 109K when most of the carbon is depleted and its abundance is lower than 16O, the 12C +16 O fusion can also become relevant. Moreover, 12C +16 O reaction can ignite also in the scenario of explosive carbon burning. The astrophysical energy region of interest thus ranges from 3 to 7.2 MeV in the center-of-mass frame. There are various measurements of the cross-section available in the literature, however, they all stop around 4 MeV, making extrapolation necessary at lower energies. To try to solve this uncertainty and corroborate direct measurement the Trojan Horse Method was applied to three-body processes 16O(14N, α24Mg)2H and 16O(14N, p27Al)2H to study the 16O(12C, α)24Mg and 16O(12C, p)27Al reactions.

The carbon-burning process in massive stars mainly occurs via the 12C +12 C. However, at temperatures higher than 109K and considering the increased abundance of 16O produced during the later stages of the heliumburning,the 12C+16O fusion can also become relevant. Moreover, 12C+16O also plays a role in the scenario of explosive carbon burning. Thus, the astrophysical energy region of interest ranges from 3 to 7.2 MeV in the center-of-mass frame. However, the various measurements of the cross-section available in the literature stop around 4 MeV, making extrapolation necessary. To solve this uncertainty and corroborate direct measurement we applied the Trojan Horse Method to three-body processes 16O(14N, α24Mg)2H and 16O(14N, p27Al)2H to study the 12C(16O, α)24Mg and 12C(16O, p)27Al reactions in their entire energy region of astrophysical interest. In this contribution, after briefly describing the method used, the experiment and the preliminary phases of the data analysis will be presented and discussed.

The $$^{27}\hbox {Al}(\hbox {p},\alpha )^{24}\hbox {Mg}$$ 27 Al ( p , α ) 24 Mg reaction, which drives the destruction of $$^{27}$$ 27 Al and the production of $$^{24}\hbox {Mg}$$ 24 Mg in stellar hydrogen burning, has been investigated via the Trojan Horse Method (THM), by measuring the $$^2\hbox {H}(^{27}\hbox {Al},\alpha ^{24}\hbox {Mg})\hbox {n}$$ 2 H ( 27 Al , α 24 Mg ) n three-body reaction. The experiment covered a broad energy range ($$E_\mathrm{c.m.}\le \,1.5\,\hbox {MeV}$$ E c . m . ≤ 1.5 MeV ), aiming to investigate those of interest for astrophysics. The results confirm the THM as a valuable technique for the experimental study of fusion reactions at very low energies and suggest the presence of a rich pattern of resonances in the energy region close to the Gamow window of stellar hydrogen burning (70–120 keV), with potential impact on astrophysics. To estimate such an impact a second run of the experiment is needed, since the background due the three-body reaction hampered to collect enough data to resolve the resonant structures and extract the reaction rate.

The elastic scattering in the reaction $$^{7}$$ 7 Li+$$^{208}$$ 208 Pb was investigated in the bombarding energy range from 25 to 39 MeV. The real and imaginary parts of the optical potential were analyzed by using a phenomenological potential. A dispersion relation analysis is presented in order to investigate the threshold anomaly effect. It is concluded that $$^{7}$$ 7 Li has an intermediate behavior between the tightly bound nuclei such as $$^{16}$$ 16 O and the loosely bound nuclei such as $$^{6}$$ 6 Li where the lack of the threshold anomaly is unambiguously observed. Reaction cross sections are also extracted from the elastic scattering data and its comparison with the ones of other systems has been performed to draw hints on the effect of the breakup channel.

Gamma-ray angular distributions in oriented $$^{92}$$ Mo produced via the $$^{6}$$ Li+ $$^{89}$$ Y reaction were studied in this work. The characteristic $$\gamma $$ rays in $$^{92}$$ Mo were measured by means of the GALILEO array, which is composed of 25 Compton-suppressed HPGe detectors arranged in a nearly 2 $$\pi $$ geometry. A detailed analysis of the spin-alignment attenuation factors ( $$\alpha _2$$ ) for different excited states in $$^{92}$$ Mo was performed, by analyzing the measured angular distribution coefficients of several pure-E2 transitions. The relationship between $$\alpha _2$$ and the spin was established in $$^{92}$$ Mo and the 244-keV transition between the 5 $$^-_1$$ and 4 $$^+_1$$ states resulted to have a E1 + M2 character with a mixing ratio ( $$\delta $$ ) of $$-0.05^{+0.05}_{-0.06}$$ , consistent with shell model calculations.

In a recent experiment investigating the origin of the $$\alpha $$ particle yield in the $$^7$$ Li + $$^{144}$$ Sm system the measured $$\alpha + d$$ coincidences at a bombarding energy of 30 MeV were shown to arise from decay of the 2.186-MeV $$3^+$$ resonance of $$^6$$ Li. In this work we demonstrate that the laboratory frame $$\alpha $$ particle angular distribution extracted from these data can be well described by a standard coupled channels Born approximation calculation and, furthermore, that the mechanism is dominated by direct, one-step single neutron stripping to the $$3^+$$ resonance, as shown previously for the $$^7$$ Li + $$^{65}$$ Cu and $$^{93}$$ Nb systems.

The mechanism of reactions with weakly-bound proton-rich nuclei at energies near the Coulomb barrier is a long-standing open question owing to the paucity of experimental data. In this study, a complete kinematics measurement was performed for the proton drip-line nucleus 17F interacting with 58Ni at four energies near the Coulomb barrier. Thanks to the powerful performance of the detector array, exhaustive information on the reaction channels, such as the differential cross sections for quasielastic scattering, exclusive and inclusive breakup, as well as for fusion-evaporation protons and alphas, was derived for the first time. The angular distributions of quasielastic scattering and exclusive breakup can be described reasonably well by the continuum-discretized coupled-channels calculations. The inclusive breakup was investigated using the three-body model proposed by Ichimura, Austern, and Vincent, and results indicate the non-elastic breakup is the dominant component. The total fusion cross sections were determined by the fusion-evaporation protons and alphas. Based on the measured exclusive breakup data, the analysis of the classical dynamical simulation code PLATYPUS demonstrates that the incomplete fusion plays a minor role. Moreover, compared with 16O+58Ni, both the reaction and total fusion cross sections of 17F+58Ni exhibit an enhancement in the sub-barrier energy region, which mainly arises from couplings to the continuum states. This work indicates that the information of full reaction channels is crucially important to comprehensively understand the reaction mechanisms of weakly bound nuclear systems.

Nuclear reactions play a key role in the framework of the Big Bang Nucleosynthesis. A network of 12 principal reactions has been identified as the main path that drove the elemental nucleosynthesis in the first 20 min of the history of the Universe. Among them an important role is played by neutron-induced reactions, which, from an experimental point of view, are usually a difficult task to be measured directly. Nevertheless big efforts in the last decades have led to a better understanding of their role in the primordial nucleosynthesis network. In this work we apply the Trojan Horse Method to extract the cross section at astrophysical energies for the $$^3\text {He}$$ (n,p) $$^3\text {H}$$ reaction after a detailed study of the $$^2\hbox {H}$$ ( $$^3\text {He}$$ ,pt)H three-body process. Data extracted from the present measurement are compared with other published sets.

Background: The phenomenon of fusion hindrance may have important consequences on the nuclear processes occurring in astrophysical scenarios, if it is a general behavior of heavy-ion fusion at extreme subbarrier energies, including reactions involving lighter systems, e.g., reactions in the carbon and oxygen burning stages of heavy stars. The hindrance is generally identified by the observation of a maximum of the $S$ factor vs energy. Whether there is an $S$-factor maximum at very low energies for systems with a positive fusion $Q$ value is an experimentally challenging question.Purpose: Our aim has been to search for evidence of fusion hindrance in $^{12}\mathrm{C}+^{24}\mathrm{Mg}$ which is a medium-light system with positive $Q$ value for fusion, besides the heavier cases where hindrance is recognized to be a general phenomenon. $^{12}\mathrm{C}+^{24}\mathrm{Mg}$ is very close to the $^{16}\mathrm{O}+^{16}\mathrm{O}$ and $^{12}\mathrm{C}+^{12}\mathrm{C}$ systems that are important for the late evolution of heavy stars.Methods: The experiment has been performed in inverse kinematics using the $^{24}\mathrm{Mg}$ beam from the XTU Tandem accelerator of LNL in the energy range 26--52 MeV with an intensity of 4--8 pnA. The targets were $^{12}\mathrm{C}$ evaporations $50\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{g}/{\mathrm{cm}}^{2}$ thick, isotopically enriched to $99.9%$. The fusion-evaporation residues were detected at small angles by a $E\ensuremath{-}\mathrm{\ensuremath{\Delta}}E$-ToF detector telescope following an electrostatic beam deflector.Results: Previous measurements of fusion cross section for $^{12}\mathrm{C}+^{24}\mathrm{Mg}$ were limited to above-barrier energies. In the present experiment the excitation function has been extended down to $\ensuremath{\simeq}15\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{b}$ and it appears that the $S$ factor develops a clear maximum vs energy, indicating the presence of hindrance. This is the first convincing evidence of an $S$ factor maximum in a medium-light system with a positive fusion $Q$ value. These results have been fitted following a recently suggested method and a detailed analysis within the coupled-channels model that has been performed using a Woods-Saxon potential and including the ground state rotational band of $^{24}\mathrm{Mg}$. The coupled-channels calculations give a good account of the data near and above the barrier but overpredict the cross sections at very low energies.Conclusions: The hindrance phenomenon is clearly observed in $^{12}\mathrm{C}+^{24}\mathrm{Mg}$, and its energy threshold is in reasonable agreement with the systematics observed for several medium-light systems. The fusion cross sections at the hindrance threshold show that the highest value (${\ensuremath{\sigma}}_{s}=1.6\phantom{\rule{0.28em}{0ex}}\mathrm{mb}$) is indeed found for this system. Therefore it may even be possible to extend the measurements further down in energy to better establish the position of the $S$-factor maximum.

The breakup of 9Be is studied via an inelastic scattering experiment on a proton target at 5.6 A MeV in inverse kinematics. Two of the three cluster constituents (α and α) as well as the proton target recoil were recorded in a triple coincidence mode allowing a full kinematics approach analysis. In this respect relative α - α and α - n, Q-value and 9Be excitation spectra, energy spectra for all fragments as well as the energy spectrum of the recoil proton were reconstructed. A clear signature of the two breakup sequential modes (5He + 4He and 8Be + n) was identified via the recoiling proton reconstructed spectra together with the direct breakup decay. A strong 5He + 4He mode was observed compatible with previous beta decay experiments.

Aydın, Sezgin ( Aksaray, Yazar ), Level structures of Rn212 have been studied by in-beam γ-ray spectroscopic methods using the Bi209(Li6,3n)Rn212 reaction at beam energies of 28, 30, and 34 MeV. A number of new nonyrast states based on πh9/24 and πh9/23f7/2 configurations have been identified. A 3(-) collective state is also proposed at 2121 keV, which is most likely formed by mixing the octupole vibration with the 3- member of the πh9/23i13/2 multiplet. The level scheme is compared with large-scale shell model calculations and discussed in terms of excitations of valence protons and without contributions from the Pb208 core. An overall excellent agreement is obtained for states that can be described in this model space.

Neutron induced reactions are fundamental for the nucleosynthesis of elements in the universe. Indeed, to correctly study the reactions involved in the well-known s-process in stars, which produce about half of the elements beyond the iron peak, it is mandatory to know the neutron abundance available in those stars. The 17O(n, a)14C reaction is one of the so-called “neutron poisons” for the pro- cess and it could play an important role in the balance of the neutron abundance. The reaction is therefore investigated in the energy range of astrophysical inter- est between 0 and 350 keV in the center of mass by applying the Trojan Horse Method to the three body reaction 2H(17O, a14C)H.

Radioactive nuclei play an important role in many astrophysical scenarios,from the Big-Bang Nucleo-synthesis to the standard solar model, from quiescent burning to the most explosive events that can occur in our universe. A huge effort has been made for more than thirty years to construct facilities able to deliver beams of radioactive nuclei with increasing intensity and better quality. This contribution revises the different mechanisms and the separation techniques employed for the production of Radioactive Ion Beams.

Individuals with Mathematics Learning Disabilities have persistent mathematics underperformance but vary with respect to their cognitive profiles. The present study examined mathematics ability and achievement, and associated mathematics-specific numerical skills and domain-general cognitive abilities, in young children with Turner syndrome compared to their matched peers. We utilized two independent peer groups so that group comparisons would account for verbal skills, a hypothesized strength of girls with Turner syndrome, and nonsymbolic magnitude comparison skills, a hypothesized difference of girls with Turner syndrome. This individual matching approach afforded characterization of mathematics profiles of girls with Turner syndrome and girls without Turner syndrome that share potential key features of the Turner syndrome phenotype. Results indicated differences in mathematics ability and nonsymbolic magnitude comparison tasks between girls with Turner syndrome and peers with similar levels of verbal skill. Mathematics ability and mathematics achievement scores of girls with Turner syndrome did not differ significantly from their peers with similar levels of accuracy on a nonsymbolic magnitude comparison task. Cognitive correlates of mathematics outcomes showed disparate patterns across groups. These quantitative and qualitative differences across profiles enhance our understanding of variation in mathematics ability in early childhood and inform how mathematics skills develop in young children with or without Turner syndrome.

The use of the Trojan Horse Method (THM) appears as one of the most suitable tools for investigating nuclear processes of interest for astrophysics. THM has been demonstrated to be useful for exploring different nuclear reactions intervening both in stellar and primordial nucleosynthesis as well. Some recent results will be here discussed together with a brief discussion of the fundamental theoretical description. General details about the recently studied 7Be(n,α)4He reaction will be given.

Background: $^{58}\mathrm{Ni}+^{64}\mathrm{Ni}$ is the first case where the influence of positive $Q$-value transfer channels on subbarrier fusion was evinced, in a very well known experiment by Beckerman et al. [Phys. Rev. Lett. 45, 1472 (1980)], by comparing with the two systems $^{58}\mathrm{Ni}+^{58}\mathrm{Ni}$ and $^{64}\mathrm{Ni}+^{64}\mathrm{Ni}$. Subsequent measurements on $^{64}\mathrm{Ni}+^{64}\mathrm{Ni}$ showed that fusion hindrance is clearly present in this case. On the other hand, no indication of hindrance can be observed for $^{58}\mathrm{Ni}+^{64}\mathrm{Ni}$ down to the measured level of 0.1 mb.Purpose: Measuring deep subbarrier fusion cross sections for $^{58}\mathrm{Ni}+^{64}\mathrm{Ni}$, where the influence of positive $Q$-value transfer channels on near-barrier fusion was evidenced previously, in order to investigate whether hindrance shows up.Methods: 167--200 MeV $^{58}\mathrm{Ni}$ beams from the XTU Tandem Accelerator of INFN-Laboratori Nazionali di Legnaro were used, bombarding thin metallic $^{64}\mathrm{Ni}\phantom{\rule{4pt}{0ex}}(50\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{g}/{\mathrm{cm}}^{2})$ enriched to $99.6%$ in mass 64. An electrostatic beam deflector allowed fusion evaporation residues to be detected at very forward angles in a detector telescope.Results: The excitation function has been extended by two orders of magnitude downward. The cross sections for $^{58}\mathrm{Ni}+^{64}\mathrm{Ni}$ continue decreasing very smoothly below the barrier, down to $\ensuremath{\simeq}1\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{b}$. The logarithmic slope of the excitation function increases slowly, showing a tendency to saturate at the lowest energies. No maximum of the astrophysical $S$ factor is observed. Coupled-channel (CC) calculations using a Woods-Saxon potential and including inelastic excitations only underestimate the subbarrier cross sections by a large amount. Good agreement is found by adding two-nucleon transfer couplings to a schematical level. This behavior is quite different from what already observed for $^{64}\mathrm{Ni}+^{64}\mathrm{Ni}$ (no positive $Q$-value transfer channels available), where a clear low-energy maximum of the $S$ factor appears, and whose excitation function is overestimated by a standard Woods-Saxon CC calculation.Conclusions: No hindrance effect is observed in $^{58}\mathrm{Ni}+^{64}\mathrm{Ni}$ in the measured energy range. This trend at deep subbarrier energies reinforces the recent suggestion that the availability of several states following transfer with $Qg0$ effectively counterbalances the Pauli repulsion that, in general, is predicted to reduce tunneling probability inside the Coulomb barrier.

International audience; Sub-barrier fusion of the two near-by systems$^{36}$S +$^{50}$Ti,$^{51}$V has been measured at the Laboratori Nazionali di Legnaro (INFN). Motivation for the experiment came from the possible effect of the non-zero spin of the ground state of the$^{51}$V nucleus on the sub-barrier excitation function, and in particular on the shape of the barrier distribution. No previous data were available for these two systems near the barrier. Our results show that the two measured excitation functions are very similar down to the level of 20-30μb. The same is true for the two barrier distributions. Coupled-channel calculations have been performed including the low energy excitations of both projectile and the two targets. We have indication that the low-lying levels in$^{51}$V can be interpreted in the weak-coupling scheme, that is,$^{51}$V (I) =$^{50}$Ti(2$^{+}$) ⊗ p(1f$_{7/2}$) and that the extra proton in the $ 1f_{7/2}$ shell does not have a significant influence on sub-barrier fusion.

In AGB environment, Fluorine and Sodium production and destruction pathways are still not completely understood: their abundances are therefore still matter of debate. \(^{19}\mathrm {F}\) (only stable isotope of fluorine) abundance is strongly related to standard and extra-mixing processestype typical of the interior AGB-stars. Furthermore, the destruction channels for this element are far from being well understood. About \(^{23}\)Na, its presence in Globular Clusters along with the well-known anticorrelation with oxygen, underline that this element has been produced in previous generations of stars: in particular, intermediate-mass AGB stars are one of the possible candidates for its production. For this reason we studied the \(^{19}\mathrm {F}\)(\(\alpha \),p)\(^{22}\mathrm {Ne}\) and \(^{23}\mathrm{Na}(\mathrm{p},\alpha )^{20}\)Ne reactions in the energy range of relevance for astrophysics via the Trojan Horse Method (THM), using the three-body reactions \(^{6}\mathrm {Li}\)(\(^{19}\mathrm {F}\), p\(^{22}\mathrm {Ne}\))d and \(^{23}\mathrm {Na}\) (d, pn)\(^{20}\mathrm {Ne}\).

Studying interactions of radioactive ions with neutrons is particularly demanding and has been performed only in a few cases. Some of these interactions are crucial in several astrophysical contexts. In the present work, the case of the 7Be destruction induced by the (n, α) reaction is investigated at the energies typical of the primordial nucleosynthesis by means of the Trojan Horse Method applied to the 2H(7Be, αα)p quasi-free reaction. The 7Be(n, α)4He cross-section has been measured in a single experiment from ∼2 MeV down to cosmological energies. The corresponding deduced reaction rate has been adopted to evaluate the impact on big bang nucleosynthesis and on the lithium problem., This work has been partially supported by the Italian Ministry of the University under grant RBFR082838 and "LNS-Astrofisica Nucleare (fondi premiali)." J.M. and G.D'A. acknowledge MEYS, under the project SPIRAL2-CZ, EF16-013/0001679. C.A.B. acknowledges support from the U.S. NSF grant No 1415656 and the U.S. DOE grant No. DE-FG02-08ER41533. S.H. acknowledges "JSPS KAKENHI (grant No. 15K17631)."

We report on the development of a new, portable detector array for charged particles with a low detection threshold to study the reaction mechanisms of exotic nuclear systems at energies around the Coulomb barrier. In order to identify both light and heavy particles simultaneously, the array consists of ten units of $ \Delta E$-$ E_{\mathrm{R}}$ telescopes, where each one is made up of four detection layers: one ionization chamber, one 40 (or 60)μm double-sided silicon strip detector and two quadrant silicon detectors with thicknesses of 300μm and 1000 (or 1500)μm, respectively. The frame of the ionization chamber is innovatively designed with printed circuit boards, thus the mass of each telescopic unit was reduced significantly which eases transport and installation requirements to different radioactive ion beam lines around the globe. The commissioning experiments focused on elucidating several reaction mechanisms encountered in the 17F + 58Ni and 17F + 208Pb systems, and we demonstrated that the array has a sufficient capability to enable charged particle identification over a large range of Z. Light particles like p, d, $ \alpha$ as well as heavy ions like 16O and 17F can be clearly distinguished. Considering these properties, this newly developed array enables in-depth investigation of the novel reaction mechanisms which are manifested in the collisions of exotic nuclei with differing isotopes.

The cosmologically relevant \(^7\)Be(n,\(\alpha \))\(^4\)He has been matter of recent studies aimed at contributing to the long-standing Li-problem. Here a brief description of the twin THM investigations will be shown and the main results discussed.

A new fast ionization chamber has been designed and built at the National Laboratories of Legnaro (LNL) to ensure a high counting rate particle identification for fusion studies involving exotic beams up to 105 pps. To reduce the response time of the ionization chamber, a design using a series of tilted electrodes has been adopted. The readout of the fast IC was optimized and extensive tests using stable heavy-ion beams demonstrated its ability to operate at high counting rates. This feature and the much larger solid angle coverage will allow to detect fusion–evaporation residues with very high efficiency.