MY husband an I decided to get a rescue dog that is about 5-6 years old.She is part shepherd/mix.She is so calm and relaxed and that was one of the things we liked about her but after a couple of days we have decided she may need to be socialized more.She will ignore us mostly and she just seems depressed.She doesn't wag her tail for food,toys,praise.We even named her Mellow because she just seems melancholi all the time.I just feel bad for her and I was wondering how we can best help her.We have a one year old blue heeler mix that wants to play with her but she just is not interested.She even has no interest in the small treats we present to her.She does eat and like her crate to sleep in at night and that's about it.We are walking her and showing her a lot of affection.Should we be doing more?

You are doing fine. No sense in trying too hard, too fast, with other people and other dogs. Keep cooing and patting and rubbing and playing, and taking her out around the neighborhood.
Depending on how long she was neglected, she may or may not change. Dogs like routine and are creatures of habit.
PS: thanks

Give her some time. I have a rescue that was the same way. Every week she got a little better, but it was almost a full2 years before she stopped cowering when I would get up or reach over to pet her. She wasn't food motivated or treat motivated at all. She hated being around other dogs and had really bad separation anxiety. With all rescues there is a honeymoon phase, I would strongly suggest getting them into obedience classes. It's a great way for the two of you to bond and for you to establish the leader role as well as building her confidence.

Just be patient, things will come along slowly but surely.

Good luck, and thank you so much for choosing the adoption option!