Singlet Channel Research Articles

Keldysh approach to the renormalization group analysis of the disordered electron liquid

We present a Keldysh nonlinear sigma-model approach to the renormalization group analysis of the disordered electron liquid. We include both the Coulomb interaction and Fermi-liquid type interactions in the singlet and triplet channels into the formalism. Based on this model, we reproduce the coupled renormalization group equations for the diffusion coefficient, the frequency, and interaction constants previously derived with the replica model in the imaginary time technique. With the help of source fields coupling to the particle-number and spin densities, we study the density-density and spin density-spin density correlation functions in the diffusive regime. This allows us to obtain results for the electric conductivity and the spin susceptibility and thereby to re-derive the main results of the one-loop renormalization group analysis of the disordered electron liquid in the Keldysh formalism.

Superconducting pairing in the spin-density-wave phase of iron pnictides

Some of the iron pnictides show coexisting superconductivity and spin-density-wave order. We study the superconducting pairing instability in the spin-density-wave phase. Assuming that the pairing interaction is due to spin fluctuations, we calculate the effective pairing interactions in the singlet and triplet channels by summing the bubble and ladder diagrams taking the reconstructed band structure into account. The leading pairing instabilities and the corresponding superconducting gap structures are then obtained from the superconducting gap equation. We illustrate this approach for a minimal two-band model of the pnictides. Analytical and numerical results show that the existence of propagating magnons in the spin-density-wave phase strongly enhances the pairing in both the singlet and the spin s_z=0 triplet channel. Over a limited parameter range, a spin s_z=0 triplet p_x-wave state is the dominant instability. It competes with various singlet states, which have mostly s^\pm-type structures. We analyze the effect of various symmetry-allowed interactions on the pairing in some detail.

A two‐step reaction scheme leading to singlet carbene species that can be detected under matrix conditions for the reaction of Zr(3F) with either CH3F or CH3CN

The results obtained from CASSCF-MRMP2 calculations are used to rationalize the singlet complexes detected under matrix-isolation conditions for the reactions of laser-ablated Zr((3)F) atoms with the CH3F and CH3CN molecules, without invoking intersystem crossings between electronic states with different multiplicities. The reaction Zr((3)F) + CH3 F evolves to the radical products ZrF· + ·CH3. This radical asymptote is degenerate to that emerging from the singlet channel of the reactants Zr((1)D) + CH3 F because they both exhibit the same electronic configuration in the metal fragment. Hence, the caged radicals obtained under cryogenic-matrix conditions can recombine through triplet and singlet paths. The recombination of the radical species along the low-multiplicity channel produces the inserted structures H3C-Zr-F and H2C=ZrHF experimentally detected. For the Zr((3)F) + CH3 CN reaction, a similar two-step reaction scheme involving the radical fragments ZrNC· + ·CH3 explains the presence of the singlet complexes H C-Zr-NC and H2 C=Zr(H)NC revealed in the IR-matrix spectra upon UV irradiation.

ΛΛ4H in halo effective field theory

The ${}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.28em}{0ex}}\phantom{\rule{1.0pt}{0ex}}4}$H bound state and the $S$-wave hypertriton(${}_{\ensuremath{\Lambda}}^{\phantom{\rule{0.16em}{0ex}}3}$H)-$\ensuremath{\Lambda}$ scattering in spin singlet and triplet channels below the hypertriton breakup momentum scale are studied in halo/cluster effective field theory at leading order by treating the ${}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.28em}{0ex}}\phantom{\rule{1.0pt}{0ex}}4}$H system as a three-cluster ($\ensuremath{\Lambda}$-$\ensuremath{\Lambda}$-deuteron) system. In the spin singlet channel, the amplitude is insensitive to the cutoff parameter ${\ensuremath{\Lambda}}_{c}$ introduced in the integral equation, and we find that there is no bound state. In this case, the scattering length of the hypertriton-$\ensuremath{\Lambda}$ scattering is found to be ${a}_{0}^{}=16.0\ifmmode\pm\else\textpm\fi{}3.0$ fm. In the spin triplet channel, however, the amplitude obtained by the coupled integral equations is sensitive to ${\ensuremath{\Lambda}}_{c}$, and we introduce the three-body contact interaction ${g}_{1}^{}({\ensuremath{\Lambda}}_{c})$. After phenomenologically fixing ${g}_{1}^{}({\ensuremath{\Lambda}}_{c})$, we find that the correlation between the two-$\ensuremath{\Lambda}$ separation energy ${B}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}$ from the ${}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.28em}{0ex}}\phantom{\rule{1.0pt}{0ex}}4}$H bound state and the scattering length ${a}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{}$ of the $S$-wave $\ensuremath{\Lambda}$-$\ensuremath{\Lambda}$ scattering is significantly sensitive to the value of ${\ensuremath{\Lambda}}_{c}$.

Quarkonium production in high energy proton-nucleus collisions: CGC meets NRQCD

We study the production of heavy quarkonium states in high energy proton-nucleus collisions. Following earlier work of Blaizot, Fujii, Gelis, and Venugopalan, we systematically include both small $x$ evolution and multiple scattering effects on heavy quark pair production within the Color Glass Condensate (CGC) framework. We obtain for the first time expressions in the Non-Relativistic QCD (NRQCD) factorization formalism for heavy quarkonium differential cross sections as a function of transverse momentum and rapidity. We observe that the production of color singlet heavy quark pairs is sensitive to both "quadrupole" and "dipole" Wilson line correlators, whose energy evolution is described by the Balitsky-JIMWLK equations. In contrast, the color octet channel is sensitive to dipole correlators alone. In a quasi-classical approximation, our results for the color singlet channel reduce to those of Dominguez et. al. [1]. We compare our results to those obtained combining the CGC with the color evaporation model and point to qualitative differences in the two approaches.

Pathways between superoxide and peroxide species on small La-O clusters

Density functional theory calculations were used to investigate the connection between superoxide and peroxide species on La-O clusters. In the singlet state, a superoxide species can transition into a peroxide species by moving through a substantial energy barrier via a series of ozonides. In the triplet state, there is no connection between the two species, although there are two paths (singlet and triplet) that allow the interaction and subsequent transformation of two superoxide molecules on a La-O cluster. The superoxide species readily transitions to a peroxide species through a triplet pathway (O 2 − + O 2 − ↔ O 2 2− + O 2 ), in which the superoxide species undergoes rapid exchange with the peroxide. In the singlet path, however, the superoxide species must move through a pronounced energy barrier to change into a peroxide species, demonstrating that these oxygen species are highly stable in the singlet state. Superoxide species over La-O clusters are in rapid exchange with peroxide species in the triplet channel while superoxide and peroxide species are both relatively stable in the singlet channel.

Carbon dioxide photolysis from 150 to 210 nm: Singlet and triplet channel dynamics, UV-spectrum, and isotope effects

We present a first principles study of the carbon dioxide (CO2) photodissociation process in the 150- to 210-nm wavelength range, with emphasis on photolysis below the carbon monoxide + singlet channel threshold at ~167 nm. The calculations reproduce experimental absorption cross-sections at a resolution of ~0.5 nm without scaling the intensity. The observed structure in the 150- to 210-nm range is caused by excitation of bending motion supported by the deep wells at bent geometries in the and potential energy surfaces. Predissociation below the singlet channel threshold occurs via spin-orbit coupling to nearby repulsive triplet states. Carbon monoxide vibrational and rotational state distributions in the singlet channel as well as the triplet channel for excitation at 157 nm satisfactorily reproduce experimental data. The cross-sections of individual CO2 isotopologues ((12)C(16)O2, (12)C(17)O(16)O, (12)C(18)O(16)O, (13)C(16)O2, and (13)C(18)O(16)O) are calculated, demonstrating that strong isotopic fractionation will occur as a function of wavelength. The calculations provide accurate, detailed insight into CO2 photoabsorption and dissociation dynamics, and greatly extend knowledge of the temperature dependence of the cross-section to cover the range from 0 to 400 K that is useful for calculations of propagation of stellar light in planetary atmospheres. The model is also relevant for the interpretation of laboratory experiments on mass-independent isotopic fractionation. Finally, the model shows that the mass-independent fractionation observed in a series of Hg lamp experiments is not a result of hyperfine interactions making predissociation of (17)O containing CO2 more efficient.

Photosensitized Generation of Singlet Oxygen from Re(I) Complexes: A Photophysical Study Using LIOAS and Luminescence Techniques

Quantum yields and efficiencies of (1)O2 ((1)Δg) production along with photophysical properties for a number of Re(I) complexes in acetonitrile solutions are reported. Two different classes of Re(I) complexes, L(S)-CO2-Re(CO)3(bpy) (L(S) = 2-pyrazine, 2-naphthalene, 9-anthracene, 1-pyrene, 2-anthraquinone) and XRe(CO)3L (X = CF3SO3, py; L = bpy, phen), were probed as photosensitizers for (1)O2 ((1)Δg) production in air-saturated acetonitrile solutions. Depending on the nature of the Re(I) complex, the excited state responsible for the generation of (1)O2 ((1)Δg) is either a metal-to-ligand charge transfer ((3)MLCT) or a ligand centered ((3)LC) state. With L(S)-CO2-Re(CO)3(bpy) complexes, (1)O2 ((1)Δg) is produced by oxygen quenching of (3)LC states of anthracene and pyrene with high quantum yields (ΦΔ between 0.8 and 1.0), while the complexes bearing the ligands L(S) = 2-anthraquinone, 2-pyrazine, and 2-naphthalene did not yield (1)O2. XRe(CO)3L complexes generate (1)O2 ((1)Δg) mainly by oxygen quenching of their (3)MLCT luminescence with an efficiency of (1)O2 ((1)Δg) formation close to unity. Bimolecular rate constants for the quenching of the XRe(CO)3L complexes' emission by molecular oxygen range between 1 × 10(9) and 2 × 10(9) M(-1) s(-1), and they are all ≤ (1/9)kd, in good agreement with the predominance of the singlet channel in the mechanism of (1)O2 ((1)Δg) generation using these Re(I) complexes as photosensitizers. All the experimental singlet oxygen efficiencies are consistent with calorimetric and luminescence data for the studied complexes. With L(S)-CO2-Re(CO)3(bpy) complexes, calorimetric experiments were utilized in the calculation of the quantum yields of triplet formation; namely φT = 0.76 and 0.83 for the triplet states of anthracene and pyrene, respectively.

Zero-energy neutron–triton and proton–Helium-3 scattering with EFT(π̸)

Model-independent constraints for the neutron–triton and proton–Helium-3 scattering lengths are calculated with a leading-order interaction derived from an effective field theory without explicit pions. Using the singlet neutron–proton scattering length, the deuteron-, and triton binding energy as input, the predictions as(t–n)=9.2±2.6 fm, at(t–n)=7.6±1.6 fm, asC(He3–p)=3.6±0.32 fm, and atC(He3–p)=3.1±0.23 fm are obtained.The calculations employ the resonating group method and include the Coulomb interaction when appropriate. The theoretical uncertainty is assessed via a variation of the regulator parameter of the short-distance interaction from 400 MeV to 1.6 GeV. The phase-shift and scattering-length results for the proton–Helium-3 system are consistent with a recent phase shift analysis and with model calculations. For neutron–triton, the results for the scattering lengths in both singlet and triplet channels are significantly smaller than suggested by R-matrix and partial-wave-analysis extractions from data.For a better understanding of this discrepancy, the sensitivity of the low-energy four-body scattering system to variations in the neutron–neutron and proton–proton two-nucleon scattering lengths is calculated. Induced by strong charge-symmetry-breaking contact interactions, this dependence is found insignificant. In contrast, a strong correlation between the neutron–triton scattering length and the triton binding energy analogous to the Phillips line is found.

Long‐Lived Charge Separation in Novel Axial Donor–Porphyrin–Acceptor Triads Based on Tetrathiafulvalene, Aluminum(III) Porphyrin and Naphthalenediimide

Two self-assembled supramolecular donor-acceptor triads consisting of Al(III) porphyrin (AlPor) with axially bound naphthalenediimide (NDI) as an acceptor and tetrathiafulvalene (TTF) as a secondary donor are reported. In the triads, the NDI and TTF units are attached to Al(III) on opposite faces of the porphyrin, through covalent and coordination bonds, respectively. Fluorescence studies show that the lowest excited singlet state of the porphyrin is quenched through electron transfer to NDI and hole transfer to TTF. In dichloromethane hole transfer to TTF dominates, whereas in benzonitrile (BN) electron transfer to NDI is the main quenching pathway. In the nematic phase of the liquid crystalline solvent 4-(n-pentyl)-4'-cyanobiphenyl (5CB), a spin-polarized transient EPR spectrum that is readily assigned to the weakly coupled radical pair TTF(.+)NDI(.-) is obtained. The initial polarization pattern indicates that the charge separation occurs through the singlet channel and that singlet-triplet mixing occurs in the primary radical pair. At later time the polarization pattern inverts as a result of depopulation of the states with singlet character by recombination to the ground state. The singlet lifetime of TTF(.+)NDI(.-) is estimated to be 200-300 ns, whereas the triplet lifetime in the approximately 350 mT magnetic field of the X-band EPR spectrometer is about 10 μs. In contrast, in dichloromethane and BN the lifetime of the charge separation is <10 ns.

Sommerfeld effect in heavy quark chemical equilibration

The chemical equilibration of heavy quarks in a quark-gluon plasma proceeds via annihilation or pair creation. For temperatures T much below the heavy quark mass M, when kinetically equilibrated heavy quarks move very slowly, the annihilation in the colour singlet channel is enhanced because the quark and antiquark attract each other which increases their probability to meet, whereas the octet contribution is suppressed. This is the so-called Sommerfeld effect. It has not been taken into account in previous calculations of the chemical equilibration rate, which are therefore incomplete for T < alphas^2 M. We compute the leading-order equilibration rate in this regime; there is a large enhancement in the singlet channel, but the rate is dominated by the octet channel, and therefore the total effect is small. In the course of the computation we demonstrate how operators that represent the annihilation of heavy quarks in non-relativistic QCD can be incorporated into the imaginary-time formalism.

The dependence of complex refractive index for four-level atom on radiation frequencies

The spectral analysis of refractive index for four-level configuration is done for dye molecules with a Gaussian form of coincident mirror-symmetric absorption and emission bands in both principal singlet⿿singlet and excited triplet⿿triplet channels. The optimum values of extinction coefficient in both channels are achieved at frequency tuning near the center of absorption band for each channel. The radiation frequencies in principal η12⿿±2 and in excited ⿿1<η34<1 channels are required to achieve the extreme values of refractive index in principal channel. The extreme values of refractive index in excited channel occur at frequencies ⿿1<η12<1 and η34⿿±1.4.

Ozone Photodissociation: Isotopic and Electronic Branching Ratios for Symmetric and Asymmetric Isotopologues

We present new calculations of the branching ratios between the various electronic and isotopic photodissociation channels of ozone. Special emphasis is placed on the isotopic/isotopologue differences because the contribution of the ozone photodissociation to the oxygen isotope and ozone isotopologue enrichments or fractionations is important for atmospheric applications. These branching ratios, which depend on photon energy, have been calculated with a full quantum mechanical wavepacket propagation approach: the multiconfiguration time-dependent Hartree (MCTDH) method. Five ozone isotopologues are considered: three symmetric, (16)O(3) (noted 666), (16)O(17)O(16)O (676), and (16)O(18)O(16)O (686); two asymmetric, (16)O(2)(17)O (noted 667) and (16)O(2)(18)O (668). The 668 and 667 asymmetric isotopologues can dissociate into either 66 + 8 or 68 + 6 for 668 and into 66 + 7 or 67 + 6 for 667. In the ranges of the Chappuis and Hartley bands, the dissociation is very fast and electronic and isotopic branching ratios are obtained from the wavepacket fluxes through complex absorbing potentials (CAPs) located perpendicular to the dissociation channels of the potential energy surfaces (PESs) of the A (1)B(1) (Chappuis) and B 3(1)A' (Hartley/Huggins) electronic states. In the range of the Huggins band the dissociation is much slower and the isotopic branching ratios of 667 and 668 asymmetric isotopologues, (e.g; 668 → 66 + 8 or 86 + 6) are obtained from the ratios of two partial absorption cross sections corresponding to the selective excitation of one or the other of the two isomers of C(s) symmetry, which dissociate respectively into 66 + 8 and 86 + 6. We find that the photodissociation of the 668 asymmetric isotopologue favors the 68 + 6 channel with a propensity varying between 52% (Hartley) and 54% (Huggins) as a function of the photon energy. The electronic branching ratios to the singlet channel (O(3) + hυ → O((1)D) + O(2)((1)Δ)) are all close to 90% above ≈32,000 cm(-1). Below this energy, the singlet channel is energetically closed and only the triplet channel (O(3) + hυ → O((3)P) + O(2)((3)Σ)) is open. These branching ratios are required to calculate the photolysis rates of each ozone isotopologue, which in turn contribute to the atomic oxygen and the ozone isotopic enrichments in the atmosphere.

Structure and interactions of ultracold Yb ions and Rb atoms

In order to study ultracold charge-transfer processes in hybrid atom-ion traps, we have mapped out the potential-energy curves and molecular parameters for several low-lying states of the Rb, Yb${}^{+}$ system. We employ both a multireference configuration interaction and a full configuration interaction (FCI) approach. Turning points, crossing points, potential minima, and spectroscopic molecular constants are obtained for the lowest five molecular states. Long-range parameters, including the dispersion coefficients, are estimated from our ab initio data. The separated-atom ionization potentials and atomic polarizability of the ytterbium atom (${\ensuremath{\alpha}}_{d}=128.4$ atomic units) are in good agreement with experiment and previous calculations. We present some dynamical calculations for (adiabatic) scattering lengths for the two lowest (Yb, Rb${}^{+}$) channels that were carried out in our work. However, we find that the pseudopotential approximation is rather limited in validity and only applies to nK temperatures. The adiabatic scattering lengths for both the triplet and singlet channels indicate that both are large and negative in the FCI approximation.

Short-range nuclear forces in singlet channels

Continuing our effort to build a consistent power counting for chiral nuclear effective field theory (EFT), we discuss the subleading contact interactions, or counterterms, in the singlet channels of nucleon-nucleon scattering, with renormalization group invariance as the constraint. We argue that the rather large cutoff error of the leading amplitude requires $\mathcal{O}(Q)$ of the EFT expansion to be nonvanishing, contrary to Weinberg's original power counting. This, together with the ultraviolet divergences of two-pion exchanges in the distorted-wave expansion, leads to enhancement of the ${}^{1}{S}_{0}$ counterterms and results in a pionless-theory-like power counting for the singlet channels.

The ultraviolet photodissociation of CS2: The S(1D2) channel

The photodissociation of CS(2) has been investigated using velocity-map ion imaging of the S((1)D(2)) atomic photofragments following excitation at 193 nm and at longer wavelengths close to the S((1)D(2)) channel threshold. The experiments probe regions both above and below the energetic barrier to linearity on the (1)Σ(u) (+)((1)B(2)) potential energy surface. The imaging data in both regions indicate that the electronic angular momentum of the S((1)D(2)) atom products is unpolarized, but also reveal different dissociation dynamics in the two regions. Excitation above the barrier to linearity yields an inverted CS((1)Σ(+)) vibrational population distribution, whereas the long-wavelength state-to-state results following excitation below the barrier reveal CS((1)Σ(+))(v, J) coproduct state distributions which are consistent with a statistical partitioning of the energy. Below the barrier, photofragment excitation spectra point to an enhancement of the singlet channel for K = 1, relative to K = 0, where K is the projection of the angular momentum along the principal axis, in agreement with previous work. However, the CS cofragment product state distributions are found to be insensitive to K. It is proposed that dissociation below the barrier to linearity occurs primarily on a surface with a significant potential energy well and without an exit channel barrier, such as that for the ground electronic state. However, oscillatory structure is also observed in the kinetic energy release distributions, which is shown to be consistent with a mapping of parent molecule bending motion. This could indicate the operation of competing direct and indirect dissociation mechanisms below the barrier to linearity.

Effect of hidden color channels on the nucleon-nucleon interaction

In the framework of constituent quark model, the effect of hidden color channels on the nucleon-nucleon ($NN$) interaction is studied. By adjusting the color confinement strength between the hidden color channels and color singlet channels and/or between the hidden color channels and hidden color channels, the experimental data of $S$ to $I$ partial-wave phase shifts of $NN$ scattering can be fitted well. The results show that the hidden color channel coupling might be important in producing the intermediate-range attraction of $NN$ interaction. The deuteron properties and dibaryon candidates have also been studied with this model.

Two-nucleon bound states in quenched lattice QCD

We address the issue of bound state in the two-nucleon system in lattice QCD. Our study is made in the quenched approximation at the lattice spacing of a = 0.128 fm with a heavy quark mass corresponding to m_pi = 0.8 GeV. To distinguish a bound state from an attractive scattering state, we investigate the volume dependence of the energy difference between the ground state and the free two-nucleon state by changing the spatial extent of the lattice from 3.1 fm to 12.3 fm. A finite energy difference left in the infinite spatial volume limit leads us to the conclusion that the measured ground states for not only spin triplet but also singlet channels are bounded. Furthermore the existence of the bound state is confirmed by investigating the properties of the energy for the first excited state obtained by 2x2 diagonalization method. The scattering lengths for both channels are evaluated by applying the finite volume formula derived by Luscher to the energy of the first excited states.

Quantum magnetism in ultracold alkali and alkaline-earth fermion systems with symplectic symmetry

We numerically study quantum magnetism of ultra-cold alkali and alkaline-earth fermion systems with large hyperfine spin $F=3/2$, which are characterized by a generic $Sp(N)$ symmetry with N=4. The methods of exact diagonalization (ED) and density-matrix-renormalization-group are employed for the large size one-dimensional (1D) systems, and ED is applied to a two-dimensional (2D) square lattice on small sizes. We focus on the magnetic exchange models in the Mott-insulating state at quarter-filling. Both 1D and 2D systems exhibit rich phase diagrams depending on the ratio between the spin exchanges $J_0$ and $J_2$ in the bond spin singlet and quintet channels, respectively. In 1D, the ground states exhibit a long-range-ordered dimerization with a finite spin gap at $J_0/J_2>1$, and a gapless spin liquid state at $J_0/J_2 \le 1$, respectively. In the former and latter cases, the correlation functions exhibit the two-site and four-site periodicities, respectively. In 2D, various spin correlation functions are calculated up to the size of $4\times 4$. The Neel-type spin correlation dominates at large values of $J_0/J_2$, while a $2\times 2$ plaquette correlation is prominent at small values of this ratio. Between them, a columnar spin-Peierls dimerization correlation peaks. We infer the competitions among the plaquette ordering, the dimer ordering, and the Neel ordering in the 2D system.

BCS-BEC crossover induced by a synthetic non-Abelian gauge field

We investigate the ground state of interacting spin-$\half$ fermions (3D) at a finite density ($\rho \sim \kf^3$) in the presence of a uniform non-Abelian gauge field. The gauge field configuration (GFC) described by a vector $\blam \equiv (\lambda_x, \lambda_y, \lambda_z)$, whose magnitude $\lambda$ determines the gauge coupling strength, generates a generalized Rashba spin-orbit interaction. For a weak attractive interaction in the singlet channel described by a small negative scattering length $(\kf |\as| \lesssim 1)$, the ground state in the absence of the gauge field ($\lambda=0$) is a BCS (Bardeen-Cooper-Schrieffer) superfluid with large overlapping pairs. With increasing gauge coupling strength, a non-Abelian gauge field engenders a crossover of this BCS ground state to a BEC (Bose-Einstein condensate) ground state of bosons even with a weak attractive interaction that fails to produce a two-body bound state in free vacuum. For large gauge couplings $(\lambda/\kf \gg 1)$, the BEC attained is a condensate of bosons whose properties are solely determined by the gauge field (and not by the scattering length so long as it is non-zero) -- we call these bosons "rashbons". In the absence of interactions ($\as = 0^-$), the shape of the Fermi surface of the system undergoes a topological transition at a critical gauge coupling $\lambda_T$. For high symmetry gauge field configurations we show that the crossover from the BCS superfluid to the rashbon BEC occurs in the regime of $\lambda$ near $\lambda_T$. In the context of cold atomic systems, this work makes an interesting suggestion of obtaining BCS-BEC crossover through a route other than tuning the interaction between the fermions.